,L'- - I' rF k-/ )II THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING Radiation Laboratory INFLIGHT AIRCRAFT VIBRATION MODES AND THEIR EFFECT ON AIRCRAFT RADAR CROSS-SECTION Final Technical Report August 1977-August 1978 Prepared By: 2 William J. Anderson ^ Dipak L. Sengupta Sanjay Correa April, 1979 Prepared for: Rome Air Development Center Griffiss Air Force Base, New York 13441 15787-1-F = RL-2283 Ann Arbor, Michigan

CU i F ' -.' r EOR OFCC; Ni-N AGE ~ L*'~ K TIJN PAGE: READ INSTRU'-CTIONS | 3I-'FORE tCOMPLET:NC, FORN t REP,:C " A JE-.,J E-t-: 'i2. GOVT ACCESSION NO. 3. RECIPiENT'S CATALOG NUMBER LA'.C- TR-79-72 i___!_____ ___________________ TiTFLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED:NFLIGHT AIRCRAFT VIBRATION MODES AND THEIR Final Technical Report:FFECT ON AIRCRAFT RADAR CROSS-SECTION August 1977 - August 1978 6. PERFORMING ORG. REPORT NUMBER N/A AUTHO R(s) 8. CONTRACT OR GRANT NUMBER(s) William J. Anderson )ipak Sengupta F19628-77-C-0232 anjay Correa PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS;he University of Michigan Radiation Lab +072 East Engineering Building 61102F inn Arbor MI 48109 2305J424 CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE )eputy for Electronic Technology (RADC/EEC) April 1979 ianscom AFB MA 01731 13. NUMBER OF PAGES MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) *ame UNCLASSIFIED 15a. DECLASSIFICATION/DOWNGRADING / SCHEDULE _________________________________________ N/A DISTHIBUTION STATEMENT (of this Report) )istribution limited to U.S. Government agencies only; test and evaluation; kpril 1979. Other requests for this document must be referred to RADC/EEC, ianscom AFB MA 01731.. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) Same SUPPLEMENTARY NOTES RADC Project Engineer: John F. Lennon/EEC KEY WORDS (Continue on reverse side if necessary and identify by block number) Vibration Aeroelasticity Surveillance Turbulence Cross-section Radar Signature Aircraft Mode Identification Radar Dynamic RCS Structural Dynamics Gust ABSTRACT (Continue on reverse side if necessary and identify by block number) A theoretical study is done for the identification of aircraft by type through elastic inflight modes and their radar signature. Three contemporary U.S. fighter and fighter-bomber aircraft are studied for inflight vibration amplitudes due to sharp-edged gusts and random turbulence. The resulting elastic and rigid body motions are found to be relatively small and at relatively low frequencies for radar detection. The rigid body response to turbulence at frequencies above 2 hz for these aircraft is found to be less than 0.01 inch rms over 95 percent of the flight path. -j FORM 1473 ) 1 JAN 73 1473 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

',- urKI Trv CL AbSIF1CATION 0P Tjji1 rP..,rWtf Data zntereoq. - _- 4IIII - -.. -. I -....... —, - -- - - - - - Response to sharp-edged gusts can be more pronounced. Elastic wing tip deflections range from 3/4" to 1/8" over 2 ft/sec. gusts; gusts of this severity are routinely observed over only 5 percent of the typical flight path. In addition to small deflections, another problem lies in the unique characterization of aircraft by their modes. For two of the three aircraft, the modal frequencies and shapes vary greatly with fuel and armament load. The third aircraft (the fighter-bomber), however, has a fundamental elastic frequenc3 which is relatively invariant with change in airspeed, fuel load and wing sweep. This mode is predominantly fuselage-bending and was used as a candidate for radar cross-section studies. Radar cross-section studies were done for varying view angles lying in the vertical plane of symmetry for the aircraft. An RCS model was based on a collection of independent scatterers identified with various components of the aircraft. Elastic deflections due to a 2 ft/sec. sharp-edged gust were observable with 3 cm radar wavelength. A number of figures are given for static and dynamic radar scattering cross-section. The frequency content of the radar return has quite strong third harmonic components at 3 cm. I Iu-r ---2-~ux.aY- IC-l 1 - -- -.1 L I -— * —u -- -~r I I - r# UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

EVALUATION 1. For noncooperative tactical aircraft identification, it is essential to get as much supportive evidence as possible to make valid decisions. Studies at RADC/EE raised the question of whether sub-structural motions of a target could generate identification information. The present study by the University of Michigan was initiated as part of a program in target modulated signatures. Its specific goal was to determine whether aeroelastic airframe motions induced by atmospheric forces could be used to obtain a radar signature. The approach involved studying the mechanical phenomena involved in such interactions to obtain data about the frequencies, mode shapes, and displacements for three classes of tactical aircraft. The variations that occur for ranges of velocity, fuel loading, external stores, and wing position were examined. The scope of the study was restricted; the implications of the calculated substructural motions in relation to corresponding changes of electromagnetic scattering centers were addressed only peripherally. The complexity of the vibrational patterns and the limited deflections that result would tend to make it difficult to observe characteristic modulations of a radar signal. F. LENNON,Wontract Monitor iii

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TABLE OF CONTENTS I. INTRODUCTION....................... II. TURBULENCE..................... 3 III. INFLIGHT STRUCTURAL MODES...................6 3. 1 Inflight Frequencies 6 3.2 Frequencies for Type A Aircraft 7 3.3 Frequencies for Type B Aircraft 7 3.4 Frequencies for Type C Aircraft 8 3.5 Composite Frequency Study 8 3. 6 Inflight Mode Shapes 9 3.7 "Optimal" Mode Tracking 12 IV. INVARIANCE OF INFLIGHT MODES.....................13 V. AMPLITUDE RESPONSE TO GUSTS AND TURBULENCE..... 15 5. 1 Rigid Body Response to Sharp-Edged Gusts 15 5.2 Elastic Response to Sharp-Edged Gusts 17 5.3 Dynamic Response to Continuous Atmospheric Turbulence: Rigid Body Plunging 26 5.4 Interpretation of the Aircraft Motion for RCS Work to Follow 30 VI. RADAR CROSS-SECTION (RCS) STUDIES. 31 6. 1 General Considerations 31 6.2 Scattering Model 31 6.3 Dynamic RCS 34 6.4 Scattering Model of the Aircraft 36 6. 5 Numerical Results 38 VII. CONCLUSIONS AND RECOMMENDATIONS........... 41 7. 1 Conclusions 41 7.2 Recommendations 43 7. 3 Unresolved Points 43 7.4 Acknowledgement 44 VIII. REFERENCES...................... 45 IX. TABLE........................ 47 X. FIGURES........... 48 APPENDIX. BIBLIOGRAPHY.................. 89 v

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I. INTRODUC TION This report covers theoretical studies of structural motion, aeroelastic vibration and radar scattering characteristics of aircraft subject to gusts and turbulence. Three aircraft have been chosen as test cases, a variable configuration fighter/bomber (hereafter called Type A and typified by the F-lll), a swept-wing fighter (Type B, typified by the F-4) and a small fighter with relatively straight wings (Type C, typified by the F-5). The weights of these aircraft are given in Table I. The weight range studied varies from 77, 302 lb. (Type A, with wet wing and fuselage) to 15, 265 (Type C). The modes of vibration for these aircraft have been studied as functions of fuel load, armament load and airspeed. Both frequencies and mode shapes in flight have been determined. A major tool for this study has been the computer program "FACES, developed by the Flight Dynamics Laboratory at Wright-Patterson Air Force Base [1, 2, 3]. This program considers the elastic forces in the fuselage and wings, the inertial characteristics of the entire plane, and the aerodynamic forces on the wings (strip theory). With substantial effort and computational cost, the aerodynamic forces can be extended to the fuselage through the use of the doublet-lattice method. Strip theory has been used here, however. This report (1) studies 12 combinations of aircraft type and weight, (2) considers mode shape as well as frequency, (3) discusses the invariance of modes and frequencies, (4) establishes expected amplitudes of motion, and (5) constructs and studies a radar scattering model of the aircraft. 1

In several regards, the work done here differs from conventional structural studies of aircraft in flight. Most structural studies concentrate on stresses at the wing root, accelerations, or possibly interaction of structure and the fluid flow (as in flutter). The emphasis here, however, is on the motion of the aircraft as perceived by a distant radar site. In this regard, the internal stress, strain and accelerations of the aircraft are of no importance, whereas the displacement field is very important. 2

II. TURBULENCE A literature survey has been carried out for references on (1) atmospheric turbulence, (2) methodology for calculating elastic aircraft response to turbulence, (3) structural data and vibration characteristics of specific aircraft, (4) effects of aging on structural response. Approximately 250 references have been cited in this survey, which have been entered into a computer file for convenient modification. Twenty-five of the more relevant papers have been read, and a brief critical summary given following the references. The most often cited journals are the AIAA Journal, Journal of Aircraft and Journal of Atmospheric Sciences as well as Air Force and NASA reports. The bibliography is included as an Appendix to this report. The literature in the field of atmospheric turbulence appears to be well developed. There are also many papers available in the area of elastic aircraft response to turbulence. Papers on specific aircraft (such as the F4) are less prevalent in the open literature and the few papers on aging seem to concentrate on composites and glue strength. The literature appears to be adequate for the purpose of obtaining general information on aerodynamic motion required by the project. There are several causes of atmospheric turbulence with the primary ones being the sun's energy and the whirling motion of the earth [4]. The mechanics of turbulence involve wind shear and convection along with some manmade effects, such as wake turbulence behind aircraft. For the radar return problem, turbulence caused by convection will be of the most interest since it is the only source of excitation over most flight paths. This convective turbulence occurs in patches hovering over the earth's surface. An aircraft spends perhaps five percent of a typical flight in one or more of these patches. The patches consist of repeated patterns of convection 3

cells of which two varieties have been observed. Hardy and Ottersten [5] state: "One pattern consists of small thermal-like cells which are 1-3 km in diameter and several hundred meters in height.... The other pattern is made up of clear air Bernard-like convection cells... which are 5-10 km in diameter and 1-2 km in height...t". An airplane passing through such a turbulence patch experiences a random force field due to velocity fluctuations u, v and w in the relative velocity between aircraft and air mass. The most significant perturbation is the upward perturbation component (indeed, it is the only one considered in the related problem of sharp-edged gusts). The velocity fler'ations are approximately isotropic and a stationary random theory is usually employed. There is general agreement that von Karman has presented the best expression for power spectral density of velocity fluctuations in isotropic turbulence. The turbulence is often considered "cylindrical," i.e., constant in magnitude along the wing span. Along with the assumption of stationarity, this two-dimensional assumption makes the problem of finding aircraft response tractable. One could imagine the nonstationary random problem to be important, i.e., the short-time behavior of an airplane suddenly exposed to turbulence might be more severe than the stationary case. This has been studied by several researchers using an envelope-modulated stationary random input. Fujimora [6,7] found that sudden onset of a stationary random forcing function can cause 28% more acceleration at the aircraft center of gravity than stationary random forcing. This fact is much more of a concern in stress analysis than in the radar return problem, however, and should be ignored here. Finally, the cylindrical nature of the turbulence is examinred by Coupry [8]. He claims that spanwise variations in the turbulence cause enough carLcellation of lift to smooth out the predicted ride. For the purposes or 4

radar modulation by elastic modes, this is important because it means that simpler theories ("cylindrical" waves) will over-predict the aircraft response. There is a scale factor involved, i.e., the ratio of length of coherence over wingspan. For aircraft as large as the Concorde, the spanwise effect reduces the peak response by a factor of two. For fighter aircraft, the cylindrical assumption will probably overpredict response by about ten percent. Several solutions using classical methods have been carried out for aircraft response to continuous random turbulence and to sharp-edged gusts. (See Section V.) These provide some feeling for the amplitudes of motion. In one calculation, a type B aircraft flying at 600 mph at sea level has an rms vertical velocity in rigid-body plunging of 3 in/sec while passing through continuous, moderate turbulence with rms vertical velocity component of 6 in/ sec. In other calculations, the elastic response to a 2 ft/sec sharp-edged vertical gust is found to be less than 3/4-inch over the entire aircraft and as little as 1/8-inch in many cases. Observation of motion this small may require X-band or shorter wavelength radar. 5

III. INFLIGHT STRUCTURAL MODES AND FREQUENCIES 3.1 Inflight Frequencies The program FACES provides the natural frequencies and modes of the aircraft structure on the ground and in flight. These results stem from a solution of the coupled eigenvalue problem including effects of elastic fuselage, elastic wing, elastic stores and aerodynamic flow. The inflight frequencies are given directly in numerical tables whereas the inflight modes are given indirectly in tables of modal participation factors. A coordinate transformation must therefore be done to recover the inflight modes. No information is given in FACES about the response problem (specific motion- due to external forces); however, the eigenvalue work from it serves as the background for all such response work done here. Volume I of the FACES manual [1] illustrates many of the natural frequencies and natural mode shapes for the type B aircraft. Volume II of the FACES manual [2] gives extensive inflight modal frequency data for the type B aircraft. Inflight mode shapes are not given in these manuals, however. In the current study, the type A, B and C aircraft have been modelled using data provided by the FACES manual (type B) and by Wright-Patterson Air Force Base (types A and C). In each case the properties of the elastic wing, elastic fuselage and elastic stores are separately found and entered into the program. These data can be calculated with some accuracy and have been tabotlated in company reports on basic data for each aircraft. Perhaps the weakest a:ect of the structural model of the airplane is the choice of elastic root restraint. The stiffness of the wing carry-through structure in the fuselage is not well documented; indeed, the "attachment point" called for in the FACES program is an artifice. The root restraint, which accounts for the fuselage-w`ing * The exception is in the swing-swing aircraft where the pivot point is lite'. an attachment point. Even here, however, the properties are not tabulated in the form needed by FACES. 6

interaction, is given values that are "strictly the user's own choice" (Ferman [1], p. 93). In practice, stiffnesses about ten times the wing stiffness at the root give reasonable answers. 3.2 Frequencies for Type A Aircraft (Swing-wing Fighter Bomber) Inflight modal frequencies are given in Figures 1-5 (full forward sweep), and Figures 6-10 (full rearward sweep). A sequence of cases is studied for dry, partially fueled and fully-fueled cases. Several of the modal frequencies remain constant with airspeed; these same frequencies have mode shapes with little phase lag in time, and tend to remain relatively "pure," i.e., do not couple with adjacent modes. Figures 4 and 9 are crossplots of Figures 1-3 and 6-8 respectively, taking data at 500 knots and considering the effect of fuel load on flight frequencies. The fuel is carried internally in the fuselage and wings and has a moderate effect on the modal frequencies. The numbering system given on the curves has to do with mode shapes and will be discussed in Section 3.6. Ground vibration frequencies for forward and swept wings are shown in Figures 5 and 10 respectively. These are helpful for mode identification studies done later. 3.3 Frequencies for Type B Aircraft (Swept-wing Fighter) Inflight modal frequencies are given in Figures 11-13. Each figure has a different number of pylons and armament. Figure 11 is a partially fueled aircraft with no armament and. Figures 12 and 13 consider 4 and 8 pylons respectively. The corresponding armament is listed in Table 1. Some of the modal frequencies remain constant with airspeed, but as seen in the crossplot in Figure 14, there is a substantial drop in modal frequencies with increasing armament load on pylons. The figures include all effects of the coupled 7

elastic fuselage and elastic wing. In this particular study, the pylons were assummed rigid so as to eliminate the additional elastic degrees of freedom, which are interspersed with the dominant wing and fuselage motion and which make problems in identifying modes. The neglect of elastic pylon effects means that candidate modes for identification will have to be studied further for this complication. The fully elastic pylon cases have been run for the Type B airplane and are very difficult to interpret. Ground vibration frequencies are given in Figure 15. 3.4 Frequencies for Type C Aircraft (Straight-wing, lightweight fighter) The inflight modal frequencies are given in Figures 16-19. These frequencies are higher than for the larger aircraft. The crossplot of frequency variation with weight in Figure 19 shows a dramatic decrease of frequencies as armament load increases. This aircraft was the most sensitive of the three in this regard. The ground frequencies are shown in Figure 20. This aircraft, more than the others, poses a real threat to mode identification as armament weight changes. Both the inflight and ground frequencies become very scrambled as weight changes, which is why no connecting lines are given between data points in Figures 19 and 20. A numerical mode tracking ame-_thod to be discussed in Section 3.6 attempts to provide the continuity as.h^own in Figures 21 and 22, but is not very helpful. 3.5 Composite Frequency Study (Types A, B and C) Because there seems to be a relation between the weight of the aircraft and the modal frequencies, a composite plot of modal frequencies at 500 knots is given in Figure 23. There is no general trend in the data; however, one might speculate whether the modes of the empt-y aircraft of each fighter type might be somewhat more predi.ctable than Ihavly-loaded aircraft ~:c vz~:-. ode arc':ft

3. 6 Infight Mode Shapes The previous work has dealt primarily with modal frequencies. Let us now Lurni outr;ttent ion to the modal shapes. The inflight mode shapes are the eigenfunctions for the airplane in the presence of an airstream. These modes are aerodynamically damped at speeds below the flutter speed. Above the flutter speed, one or more of the modes are unstable and grow in amplitude with time. The previous sections considered inflight and ground frequencies (eigenvalues), and the variation of inflight frequencies with airspeed and loading (Figures 1-23). It is necessary,however,to consider the mode shapes for two reasons. The first is that the radar return depends on the relative amplitudes of different reflection points, lines and surfaces. The second is that mode tracking (following each mode as airspeed and weight change) is difficult without knowledge of mode shapes to distinguish them when frequencies are closely packed. The modes and frequencies are calculated through the idealized models shown in Sketches 1-3. The structural stiffness is developed using finite sections of beams which can be serially kinked. The inertia of fuselage and wing sections is located appropriately within each section at the center of gravity of the section. Each section has rotary as well as translational moment of inertia. The degrees of freedom are identified at section boundaries and consist of wing z deflection and torsional angle about the elastic axis, as well as fuselage vertical deflection, forward displacement and rotation about the pitch axis. The aerodynamic forces used in the model are based on strip theory, and act on the wing only (Sketch 3). Of the five available degrees of freedom at each section boundary, three are considered relevant to the radar problem for symmetric motion. These are 9

Sketch 1. Elastic model used in FACES. Beam theory. Fuselage and wing can be kinked. lumped moss Sketch 2. Finite sections used in FACES. Can be serially kinked. Three degrees of freedom at fuselage stations and two degrees of freedom at wing stations for symmetric motion. U Sketch 3. Aerodynamic model used in FACES. No aerodynaric forces on fuselage or tail. C)

the wing bending deflection, wing torsional rotation and fuselage bending deflection, as plotted in Figures 24a to 27c. These twelve figures show the fundamental mode for each of the four major geometries studied, with all at medium weight. The z deflections are in feet and the torsion is in radians. The motion in each case consists of an in-phase and leading component. The motion is not synchronous, i.e., different points along wing and fuselage are not in phase with each other. The deflection for the wing w(y,t) could be written iw.t i(w.t + 7/2) w(y,t) = f1(y)e + f2(y)e 1 for instance, where f1(y) and f2(y) are plotted as solid and dotted lines. Discussing mode shapes for a complex structure is more difficult than discussing frequencies, which are scalars. An attempt is made here to quantify the mode shapes so that modes can be "tracked" and their invariance (or lack of it) determined. The method used is to consider the maximum amplitudes in wing bending, wing torsion and fuselage bending. To compare on the basis of length scales, the wing torsional angle is multiplied by the mean half chord of the wing. This corresponds approximately to the distance the leading edge and trailing edge move vertically and is a reasonable way to judge the effect of torsion on the radar return. (Leading edges may be good reflectors.) A code for each mode shape has been worked out for a normalized vector of length 100, where the mode illustrated in Figures 24-26 would be represented by (17 02 98) t A, t '4' component of wing / — fuselage bending wing bending torsion bendg Sketch 4. Mode-shape code. 11

This mode is easily seen from the code to be dominantly fuselage bending, whereas deducing this from the figures takes some effort. Furthermore, comparisons between mode shapes can be made, and differences quantified. Using the code discussed above, the frequencies displayed in Figures 1-23 have been "tagged" with their corresponding mode shapes. 3.7 "Optimal" Mode Tracking Both modal shapes and modal frequencies change with the three parameters considered: airplane load, airspeed and wing sweep. Mode-tracking thus involves following a particular mode as any parameter is varied. The modal frequency is not a good indicator of the modal pcn-ibr, because a modal crossover upsets a notation that is frequency-ordered. This leaves the mode shape as the possible "tag" on a mode; the shape has been described with a numerical string quantifying the contributions from wing bending, wing torsion and fuselage bending. This six-digit code is used as the "tracer" in the mode-tracking process. The mode-tracking is optimized on the basis of shape. The eight "variable" modes in Sketch 5 can be permuted in 8! or 40,320 ways; each permutation represents a unique mapping of the "reference" modes onto the "variable" modes, frequency "reference" * modes "variable" c modes ~ o Parametezr of - interest Sketch 5. Permutation of modal frequencies. 12

For each of these mappings, the sum, over all eight modes, of the squares of the differences between the two-digit code numbers, for a reference mode and the variable mode, is computed. The minimum of the 40,320 sums thus obtained corresponds to the "optimal" mode-tracking; a root-mean-square error can be obtained from this minimum sum. This procedure: (1) searches for a global minimum and so often discards intuitively "comfortable" mappings between lower modes. (2) disregards the possibility of picking up variable modes from or losing reference modes to higher frequencies. Typical results of this mode-tracking procedure are illustrated for aircraft Types B and C in Figures 21 and 22. One can appreciate from these figures the difficult in tracking modes for aircraft Types B and C. If one can track the modes with enough confidence in a given case, the next question is whether the frequencies and mode shapes along the properly tracked mode are invariant or not. This is a more detailed question than tracking and is discussed in the next section. IV. INVARIANCE OF INFLIGHT MODES The information contained in Figures 1-23 is the factual basis for determining invariance for the three aircraft. The question of how to define invariance of modes is somewhat subjective, but is basically whether modal frequencies and shapes vary excessively with change in aircraft loading, speed and configuration. What is excessive from the radar return pattern is critical and cannot be completely determined at this point. Although the first 8 modes have been studied, identification doesn't require invariance of all 8 modes. The aircraft motion can be shown to be dominated by the fundamental mode with some contribution from the second and:hird modes. 13

Some generalizations to be drawn from the results include: (1) Variation of mode shape and frequency with airspeed is generally modest and could be accounted for if it were the sole effect. (2) Variation of rro de shape and frequency with fuel and armament load is great. Modes are scrambled so much that it is difficult to track them, even analytically for a given aircraft where no noise is present (at discrete, calculated points). (3) Variation of mode shape and frequency with wing sweep for the type A aircraft is not severe and could be accounted for if it were the only effect. Only the Type A aircraft appears to be a candidate for identification by invariance of an elastic mode. Its fundamental mode (fuselage bending) varies only from 5.8 to 6.8 hz with wide changes in airspeed, loading and wing sweep. Unfortunately, other fighter aircraft in the air with their profusion of frequencies can, for certain stores combinations as seen in Figure 23, mnimic the Type A aircraft elastic frequency. Therefore, one would have to search for a unique radar return due to the mode shape of the Type A aircraft. Another necessary condition for identification is that the modes in question itust be excited enough by gusts and turbulence to be observed. The amtirplitude of this response is studied in the next section. 14

V. AMPLITUDE RESPONSE TO GUSTS AND TURBULENCE Three separate gust and turbulence problems will now be considered. The purpose will be to develop insight into the amplitude of response of the aircraft. The cases studied differ in whether the airplane is considered rigid or elastic, and whether the turbulence is modelled by a sharp-edged gust or as a stationaryrandom process. Of the four possible combinations of these effects, the most complicated one (elastic response to stationary random turbulence) is not considered because of its difficulty and limited scope of this study. One can determine the major effects from the first three cases, however. 5.1 Rigid Body Response to Sharp-Edged Gusts A simple calculation of the rigid body response to a sharp-edged gust will be made. Only the plunging motion, and not pitching, will be considered. The type B aircraft will be assumed to have the following flight characteristics: mass = m = 1696 slugs weight - W = 54,600 lb. z(t) 2 wing area S = 530 ft Sketch 6. Coordinate System. speed - U = 880 ft/sec (600 mph) W(t) air density at 10,000 ft = =.000582 slugs/ft3 0 air density at sea level = = 0.002378 slugs/ft Sketch 7. Sharp-edged Gust. The lift-curve slope, C, could be calculated by procedures outlined by Roskam [9]. The procedure is somewhat involved, however; therefore, CL will be estimated at an intermediate value of C = 3.0. L The sharp-edged gust will be assumed to have intensity w = 2.0 ft/sec, 15

which corresponds to the extreme value measured at least once per ten seconds in "turbulent patches." These turbulent patches cover only five percent of the flight path, hence, this magnitude of sharp-edged gust is an upper limit to gusts that could be observed routinely. The response in plunging of a rigid aircraft to a sharp-edged gust is given by Fung [10]. For a gust velocity w(t) = w H(t) (positive upward) one obtains a response 1 -Xt z(t) - wO(l-e ) - wt where the characteristic time required to appre::n a steady motion is where p US LdC 2m da -1 For our problems, at sea level, X = 0.981 sec and at 40,000 ft, -1 A = 0.240 sec. Hence -e981t) ZS(t) = 2.039 (l-e *1) - 2t (ft, where t is in seconds) SL -.240t z40,000( = 8333 (l-e ) - 2t (ft, where t is in seconds) The solution for this plunging response is shown in Figure 28. The figure confirms the characteristic time of 1 second at sea level and 4 seconds at altitude during which the aircraft accelerates upward to a terminal velocity equal to the gust speed. The maximum acceleration of the aircraft is at t = 0 and is - w XA To o compare this acceleration with that due to gravity, one divides to get the load factor An: An - |I maxi An -- g W X o - -- e 16

At sea level An = 0.061 g. At 40,000 feet An = 0.015 g. Both values are relatively small and indicate that the gust is mild. 5.2 Eto Shar-Edged Gusts Background The vibration signatures of structures are characterized by mode shapes, frequencies and amplitudes of response to various inputs. The response is divided between the various modes, with modal content typically decreasing for the higher modes. For aircraft structures, the ambient turbulent field provides aerodynamic inputs which excite these modes. The sharp-edged gust, a simplification of the actual (random) field, provides useful information on the aircraft vibration-signature. Beyond this simplification of the input, the aircraft structure itself will be idealized as a rigid fuselage with an unswept, straight, slender wing. Arbitrary spanwise distributions of mass, stiffness and chord are allowed. The entire airplane is free in vertical translation, or 'plunging,' and the wing is elastic in bending; all torsional modes are assumed to be restrained. The modal analysis detailed here follows Bisplinghoff, et al. [11] It is to be expected that these theoretical results will overestimate the elastic response. The actual wings on the aircraft studied are swept, causing less lift per unit span and initiating lift at different times along the span. In contrast, the theory applies to a larger lift instantaneously along the entire wing, which is a more severe loading condition. The theory is intended to provide approximate values for elastic wing motion. This will serve as an indication of the wavelength of radar required 17

to observe the motion. Each of the modes will respond with its own amplitude; hence the results should distinguish between observable and nonobservable modes. Symbols bR a(y) b S m M U w (a) WG p 1 w( y,t) k;). (y) )(t) 1T Clt),*..^(t) iY - 1. M. ( ) reference semi-chord spanwise chord distribution semi-chord at station y wing area running wing-mass wing semi-span total airplane mass airplane forward velocity gust velocity profile density of ambient air total number of modes considered bending frequencies of wing, L = 0 nondimens ional time vertical displacement at station y rigid-body mode shape, 1 (y) = 1.0 shapes of vibratory modes of wing response of 'plunging' mode normal coordinates representing responses of vibratory modes Wagner function Kussner function generalized forces due to gust generalized forces due to motion prime denotes derivative with respect to the argument 18

Equations of Motion The response of the aircraft is separated into a time-dependent component (t) and a spatial component P(y), with the total response then given by n w (y,t) = Z j. (t)j ((y). j=l J The mode shapes are normalized so that Q 2 M = 2 fi m.i dy i=l,...,n. Positive coordinate directions are indicated in Sketch 8. z Sketch 8. Coordinate System. The response is given by the solution of the differential equations 2 n n A~i(s) + XQ2.i(s) + Z A ijj(s) + 2 E B..s j (o) (s-a)da 1j1 j. i j 70 w (a) = 2 b Bi - Y' (s-a)do R li 0 U i=l,...,n; eI = 0 19

where: b = a(y)bR s = Ut/bR X = M/(T p S bR),= wi b/U i i R + 2 A = (bR/S) f a(y) i j dy Bi = (bR/S) f a(y) i j dy (5.1) [Eq. 10-149, Ref. [ii].] With a step-function gust velocity input, the gust velocity profile WG (o) is wG(a) = wG(O+) = WG, which allows modification of the nonhomogeneous terms in the system of equations. From Eq. 5-382 [11], the unsteady lift due to the gust is sd wG(a) L = 27r p U b {wG(O)Y(s) + f da- (s-G)dc} G 0 which, for w (a) = WG, reduces to G G r L = 27 p U b wG(O)Y(s), s in ce d w (a) d a Y(s-a)da = 0. 0 d Hence, the spanwise lift due to the gust is LG(y,s) = 2Tr p U a(y)bR wG Y(s). The definition of generalized force due to the gust is (Eq. 10-143, Ref. [.1!)5 20

D. +Q = 7 - i LG dy or D +Q 27 p U bR wG (s)f i. a(y R G 1 From Eq. 10-142 [11], the equations of motion are 2 2 M D. i dt2 Si + Mi i i = i 1 i M. = 3 +3 Transforming to nondimensional time, U2 I + M2 + Mi 2 i ' b 2 i i bR bR )dy (5.2) D. - 1 and so M. D. +, 2 R bR i i p S U Ir p S U2 The last term becomes, on substitution from (5.2), D. bR 2 b _ R p U2 WG (s) Bi Hence, for a step-function gust velocity input and for symmetrical motion, equations (5.1) become 2 n n s () + (s) + Z Ai i(s) + 2 B.. / "(o) ( s-o)du j=l 1J J j=l 1j 0l 2 bR wG U Bli Y(s) i=l,...,n; 10 (5. 3) with b, s, A, S defined as before and 21

A.. 13 B.. lj = (2 b /S) f R 0 = (2 bR/S) f R 0 a (y) ~(ij dy a(y) 4ij. dy Rewriting (5.3) in matrix notation {E"(s)} + [, Q2 _{t(s)} + [_i {U"(s)} + 2[B]s 2[B] { "(o)} (s-o)do 0 2bR WG AU {B} I (s) where t- Q2 -a {B} [A] [B] 2 R R 2 - U2 T = [A I [Aij] = [Bi ] 13 + x ) {g"(s)} + E- Q2 _ {g(s)} 2b R wG x u (s) - [B s f { "(o)} (s-o) da 0 (5.4) Numerical Solutions Numerical solution of equations (5.4) requires some modification to the system, which is implicit in g. Define I such that S {I} = / {"(o) (s-)dao (5.5) 0 22

Hamming [12] has shown that this convolution integral has poor convergence properties unless handled carefully. The following procedure is related to Hamming's suggestion for separating out a portion of the integrand. With a sufficiently small time interval As, the displacements can be assumed constant within each interval, and a trapezoidal integration rule can be used; thus (k+l) As {I} = ( s) (k+ ) As 2 P(s-a)dO + Z {I"(iAs)} i=l J ( (i- ) As 2 (kAs-a) do (5.6) Equation (5.6) assumes that s = (k+l)As (current time) and {i"(0) } = 0 The latter is an approximation to an initial steady-flight condition. Adopting a polynomial approximation to the Wagner function ~ s+2 ~(s) = s+4 ' -cs/ s+4 it can be shown that 1 " (i+ )As J(i- 2) As (k-i- 1)As + 4 (k As-a)da = 21n 1( (k + As (k-i+ -)As + 4 (5.7) (k+l) As (k+ ) As 2 > (s-o)dc = 2 in |4 7 + As As+4 2 (5.8) Combining equations (5.6), (5.7) and (5.8), 23

k (k-i- )As+41 {I}.= {"((k+l)As)} 2 n As + + "(iAs)}(2 + 4 i=l (k-i+- )As+4 2 / (5.9) Finally, combining equations (5.4), (5.5), (5.6) and (5.9), 2bRWG k (k-i- ~)As+4 ) - {B} }((k+l)As) - 2[B] Z {"(iAs)}(2 In + As) Equations (5.11) are in a form suitable for direct integration by the Newmark method. The following algorithm may be used (Ref. [13]): A. Initial Calculations 1. Initialize {} = {0} at s = 0 {'} = {0} at s = 0 {"} = {0} at s = 0 2. Select 'time' step size As and parameters a and 6; calculate integration constants. 6 > 0.050; a > 0.25 (0.5 + 6)2 1 6 1 a0 2; al 2 ' 1s; a2 = aAs a = 4 - 1; a = - a3 = a (- 1; a4 = as 1; a 2 a6 = As (1-6); a7 = 6As. 24

3. Form mass [M] and stiffness [K] as defined by equations (5.10) and (5.11). Form effective stiffness [K]: [K] = [K] + a0[M] 4. Triangularize [K]: T [K] = [L][D][L] B. Iterative Loop 1. Calculate effective loads at s + As: s+As = {R}s+s + [M](a0{} + a2 {'} =a3{}) 2. Solve for displacements at s + As: [L][D][L] } = {R} s+As s+As 3. Calculate accelerations and velocities at s + As: { s }+As ao( { }s+As )s s 3 s {i} As { + 6"s +a7 s+As Results Each of three aircraft types was studied at the medium weight to provide typical response values. In each case, the aircraft penetrated a two fps sharp-edged gust applied instantaneously along the entire wing. The results yield elastic displacements which are rather small, ranging from 3/4-inch wing tip displacement on the type B aircraft, to response as low as 1/8-inch wing tip displacement for the type A aircraft (swing-wing fighter-bomber). Figures 29-31 show the elastic response at the wing tip. The rigid body plunging mode is not included. The bulk of the motion in all cases was due to the first aircraft mode. The second mode participates in a minor way and the third and higher modes are scarcely excited. In addition to the graphical results in these figures, a wealth of tabular output is available for each aircraft. 25

5.3 Dynamic Response to Continuous Atmospheric Turbulence: Rigid Body Plunging An airplane penetrating an atmospheric turbulence field experiences continuous rather than discrete gusts; hence a statistical approach is needed to model the continuous properties of atmospheric turbulence. The general method consists of applying a random input (the power spectrum of atmospheric turbulence) to a linear system (the mechanics of the rigid body plunging mode) and studying the response of this system. Only statistical properties of the response, e.g., root-mean-square displacements, may be determined by this method; explicit time-histories will not be known. The aircraft is modeled by a rigid wing of constant chord 2b flying at a forward velocity U. The wing thickness and the magnitude of the vertical translations are assumed small compared to the chord. The fluctuating turbulence velocities u,v,w are assumed small compared to U. The components u,v may be neglected as the wing is free in vertical translation only. Thus, the wing is subjected to a fluctuating angle of attack w a = U. U It is further assumed that the gust field is two-dimensional (no spanwise variations) and the turbulence pattern does not change during the time required for one particle of air to traverse the wing, i.e., during time 2b/U. Inpirt The turbulence w is assumed to be a stationary random function given by the von Karman power spectrum, ~((Q): 8 2 1/ - 2 1 + (1.339 L Q)I [1 + (1.339 L Q)2 26

where: Q = space frequency (rad/ft) I. = scale of turbulence (ft) = RMS gust velocity (ft/sec) W The function ~(w) satisfies the relation: 00 0 0 2 == f (w)dw. Rigid-Body Admittance To calculate the mechanical admittance of the system, the wing is subjected to a sinusoidal gust described by the real part of: - ik(s-x*) w = e G G where k is the nondimensional frequency: wb k - Ub= b. The response of the wing is given by the solution of the equation of motion: U2 M "(s) = span L dy + fp dy b2 span G span M where: M = airplane mass = normal coordinate Ut s = nondimensional time, s = b L = lift due to gust L = lift due to the motion Substituting as a solution: iks a = w e and writing the expressions for LG and iL, we have: 27

b 2K(k) wG U k[2i C(k) - (2X+l)k] where: X = M/TT p Sb 3 p = density of the air (slugs/ft ) S = wing area (ft ) C(k) = Theodorsen Function K(k) = C(k)[Jo(k) - i Jl(k)] + i J1(k) The expression for - is the admittance function with resp:ct to vertical wG displacement. Output Let P(w) be the power spectrum of the airplane response. Then ~2 oo = fS j(w)dw where j is the root-mean-square displacement. The following relation then holds: I 2 4(w) = X ~(w) Using polynomial approximations to the complex terms in the admittance expression, the power spectrum of the response becomes: b2 4|K(k)l2 2(w) (W2 U k 22i C(k) - (2X+l)k ( b 4 1 1 2 l+27rk 2 2 -2 4(w) U +27k k 4+k2 (2X+1)2 or 28

2L 2 8 Lk b2 1+ (1.339 — ) b 4 1 x_ w 3 b Uk) 2 1+2rk 2 4+k2(2+1)2 [1 + (1.339 L)211/6 b The mean-square displacement becomes: L 2 8 Lk 2 1w 1+ (1.339 —) 2 = b 4 1 TW 3 b dk 0 U2 l+27k k2 4+k2(2X+l)2 [1 + (1.339 Lk)2116/ b 4Lbo 2 oo 8 Lk 2 4Lb 1 1 + 8(1.339 — ) 4 3 b dk u2 0 +27k k2 4+k2(2X+1)2 [1 + (1.339 Lk)2111/6 b Frequency Limits The integrand in the above expression is singular at k=O; hence, a lower frequency limit (c) on the power spectrum of the response is needed. This corresponds to an artificial high-pass filter. Since radar returns are garbled at very low frequencies (less than 5 Hz), this filtering is acceptable. The mean-square displacement then becomes 8 Lk)2 C 1+ -(1.339 - 2 4Lb w 2 4 1 1 3 b 1 Tr U 0 1+27rk k2 4+k2(2X+l)2 [1 + (1.339 Lk)2]1116 b In practice, integration to a finite upper frequency limit suffices as the response becomes vanishingly small at the higher frequencies. Results The rigid body plunging responses of the three aircraft types (A,B,C: medium weight) were computed with the low frequency cutoff point as the parameter. The upper frequency cutoff was set at 100 Hz. Results are shown in Figure 32 for a root-mean-square gust velocity of 2 ft/sec. The mean-square displacement of the airplane as a whole is not large, unless one is willing to 29

attempt to detect frequencies below 1 hertz, say. 5.4 Interpretation of the Aircraft Motion for RCS Work to Follow The elastic motion of an aircraft in flight has been studied in a deterministic as well as a random approach. There is a question as to which way provides more information for identification.. The random approach of section 5.3 is not encouraging because of the small rigid body displacements which were found - approximately 0.01 inch r.m.s. when signals above 2 hz only are processed. The deterministic approach for the sharp-edged gust does not give much more hope. Peak elastic response at the wingtip Wa only 0.12" for a type A aircraft, 0.75" for a type B, and 0.33" for a type C, all at medium weight. The dominant elastic motion in response to the sharp-edged gust is in the fundamental mode (corresponding to the lowest frequency). A deterministic approach will be used in the following RCS work. The response of aircraft type A with wings fully forward will be the test case. The vertical motion of the aircraft will be assumed harmonic and consisting solely of the first elastic mode. The half-amplitude of motion of the wing tip will be taken as 0.3 cm (0.12"). This number is as large as can be reasonably inferred from Figure 29 and achieving it would require successive upward and downward gusts. The RCS calculations therefore study a motion which is an upper bound to what one could observe in typical turbulence cells occupying 5% of the earth's surface. Finally, it is noted that the type A aircraft has a relatively large fuselage displacement in the first mode as can be seen by comparing Figures 24a-c. Even if this value of 0.01 inch rms were doubled or tripled at the vwingtip due to inclusion of elastic effects, it would still be small. 30

VI. RADAR CROSS-SECTION (RCS) STUDIES Structural motion and aeroelastic vibration of aircraft subject to gusts and turbulence have been discussed in earlier chapters. The present chapter theoretically studies the effects, if any, of these aerodynamically induced motion of the aircraft on its RCS. 6. 1 General Considerations Theoretical determination of the RCS of a complex body (with regard to its electromagnetic scattering) such as an aircraft is an extremely difficult boundary-value problem in electromagnetics. A plot of the RCS versus time for an aircraft in flight often appears as a noise-like fluctuation even when the nominal aspect of the aircraft is constant. Because of the uncertainties about the aspect (due to roll, pitch, etc.), the RCS is often best described statistically in terms of various distribution functions [15,16]. In general, however, these distributions point out that there is no simple solution. to the RCS problem for all aircraft [17]. To avoid unnecessary complications we will avoid the statistical approach. Instead, we confine our attention to a deterministic study of the effects on the ambient RCS of an aircraft produced by some of its identifiable motion induced by air-turbulence, etc. The next section describes the simplified electromagnetic model of an aircraft, and how the static and dynamic cross sections are obtained. 6.2 Scattering Model The fundamental assumption of the theoretical method for obtaining the RCS of an aircraft is that electromagnetic scattering by the aircraft may be assumed to be that due to a collection of independent scatterers which may be identified with the various components of the aircraft (e.g., fuselage, wing, etc.) [18]. Usually, this is possible at sufficiently high radar frequencies 31

where the appropriate dimensions of the aircraft are large compared to the radar wavelength. To this end, the aircraft is considered to be an ensemble of components, each of which can be geometrically approximated by a simple shape in such a way that the RCS of the simple shape approximates the RCS of the component it models. Once the component scatterers are identified, their cross sections are obtained from known results. Each of the components is then replaced by a point scatterer located at its scattering (or phase) center, and having a scattering area equivalent to that of the component. Finally, the component cross sections are combined appropriately to estimate the RCS of the entire aircraft. This method has been found usofFul in the theoretical estimation of RCS of aircraft, missiles and the results have been found to be in fair agreement with measured values [19,20,21]. Let us assume that for a given combination of aircraft aspect angle, wavelength and polarization of the radar, N scattering components have been identified for which the radar cross sections are a&, 2,...,.N One of the methods of combination of these cross sections involves the relative phase angles between the scattered fields from the N scatterers. This leads to the following expression, denoted by a (cross section by relative phase), for the RCS of tlhe entire aircraft: N 1/2 (.12 a | Z (a.) exp(ir.), (6.1) p j=l wlhere G. is the crosssection of the j-th component and 3. is the relative phase J J angle associated with the radar return from the j-th component. The magnitudes of B.'s are determined by selecting a reference point (or origin) on the airJ craft and obtaining the phase angle of the return from each component from its distance from the origin. For this purpose consider a rectangular coordinate system (x,y,z) with origin at 0 which also serves as the origin of a spherical 32

polar coordinate system (r,9, ) with its polar axis oriented along the zdirection. Let the aircraft be oriented horizontally (in the y-z plane) with its nose aligned along the z-axis and its center of the fuselage located at the origin 0, as shown in Figure 33. Let the coordinates of the j-th scattering center be (xj,y.,zj). Under these assumptions it can be shown that in the radar direction (6,0 ) the phase angle.j appropriate for the j-th scatterer is given by: (3. = 2k[x. sin 6 cos (o + y. sin 6 sin $ + z. cos e ] (6.2) 27T where k = 2, X being the wavelength of the radar waves. Observe that for 0 = 0, i.e., in the x-z plane of Figure 35, Equation (6.2) reduces to 3. = 2k[x. sin e + z. cos 6 ] (6.3) c o j o which indicates that 3. is independent of the y-coordinate of the scattering center. Also, note that in the ideal case when all the returns combine in phase one obtains the maximum RCS of the aircraft as: N 1/2i 2(6.4) a = I (a.)2!4) Pmax j=l J It is evident that in the above approach one must know the distances of the scattering centers from the chosen origin. These can be estimated either from the aircraft drawings or from their scale models. However, Equation (6.2) or (6.3) indicates that the phase angle 6. depends directly upon the ratios xj/X, etc. Therefore, for a large aircraft at small wavelengths it may be impossible to obtain these distances from the drawings or models with suffi2ient accuracy [18, 19] * As an alternative to the relative phase method, there exists another iethod often referred to as the random phase method [19]. This method is 33

based upon the assumption that many different j.'s are randomly distributed, then upon averaging over B. we obtain the average RCS, denoted by a', as N a' = ~ o. (6.5) j=l 3 The deviations of the observed RCS from the average crosssection a' are characterized by employing the concept of RMS spread, denoted by S. This measure of the probable variations in cross section due to the relative phase effects leads to the bounds (a' + S) for the observed total RCS where 2 N 2 N S = ( Z a.) - o.. (6.6) j=l J j=1 3 It is evident from the above discussion that the random phase method gives estimates of the amount by which the cross section might deviate from the average value because of the phase effects. On the other hand, the relative phase method of combination not only estimates the amount by which the crosssection deviates from the average value but also the locations (in aspect or wavelength) of the relative peaks and nulls in the RCS. So far, it has been assumed that the aircraft is static and hence, the RCS values obtained from the above expressions will be independent of time an!, thus, will be referred to as the static RCS. In the next section we describe h..e method of obtaining the RCS of an aircraft undergoing vibratory motion -nduced by air turbulence. 6. 3 Dynamic RCS In earlier chapters we have obtained the frequencies and modes of vibration of the aircraft caused by air turbulence. It was found that the vertical displacement of the aircraft was significant; the mode shape and frequencies of these displacements were obtained numerically. We shall assume tha t; 34

tne scattering centers of the aircraft experience similar kinds of vertical motion in time. Thus, for any mode of vibration, the x-coordinate of the scattering center will vary in time according to that mode shape and at a frequency corresponding to that modal frequency. It should be noted that the modal shapes obtained from free vibration considerations (see Chapter III) must be scaled properly to obtain the scattering center displacements. In accordance with our earlier notation, let the x-coordinate of the j-th scattering center (associated with the wing) undergoing the i-th mode of vibration will be denoted by x. = nj cos(W.t + j.), (6.7) where, j = [fl(Yj)2 + f2(Y 1/2 (6.8) f2(y,) tan C. = f ( - (6.9) The quantities fl(Y.), f2(y.) and oa identify the shape of the induced motion of the scattering center caused by the i-th mode of radian frequency w.. Vertical motions of the scattering centers associated with the fuselage and other components are included in a similar manner. N (, t) = (a)1/2 exp(ij)|2 (6.10) P 0 j-1 with Sj = 2k[nj sin e cos o~ cos(Oit + c.j) + yj sin 0 sin Cp + z. cos 0 ], (6.11) J o where the dependence of time and radar direction are shown explicitly in a If the radar is located in the vertical x-z plane, ~0 = 0, the RCS expression 35

reduces to: N o-(0O t) E (a.)1/2 exp i 2k[nj sin 0 cos(w.t + a.) + z. cos e ]12 (6.12) Note that with this model, the nose-on (6 =0) RCS of the aircraft is unaffected by the vibration. 6.4 Scattering Model of the Aircraft Aerodynamic studies, discussed in earlier chapters, indicated that the vibration mode of type A aircraft is reasonably invariant to airspeed, fuel load and wing sweep. For this reason we have chosen to st-udy tLie RCS of the aircraft model F-lll which belongs to type A., ie component scatters and the location of the corresponding scattering centers are obtained by studying a 1/72-scale model of the aircraft. The orientation of the aircraft is as shown in Figure 33 and it will be assumed that the radar is located in the x-z plane. Dominant scattering components are identified from a study of the scale model. The approximate geometrical shapes and the corresponding theoretical expressions for their cross sections are as follows [18-21]: (i) The nose of the aircraft is approximated by a section of a conducting paraboloid. This component will contribute (a ) in the range 0 < 0 < 74~. It's contribution is obtained from: (o) = sec4 9. (-.13) (ii) The main body of the fuselage is approximated by a conductive circular cylinder of length L = 19.72 m and radius a = 1.08 m. This will contribute in the range 74~ < 9 < 140~. It's contribution (a2) is determined by using the following expressions: 36

X a sin 0 0c (Q ) = o 740 < 6 < 85~ (6,14a) 2o 2 2 ' -- 87~r Cos 0 0 2 2(r/2) =2 L a, for 95~ < e < 140~ (6.14b) 2 X - O - (iii) Each of the two wings is approximated by a conducting rectangular plate oriented in the y-z plane. Each plate has dimensions W and L in the y and z directions, respectively. The combined contribution (a3) from the two wings is obtained from: 2 W2L2 2 sin (kL cos 9 ) o3(eo) = 2 sin e (6.15) 2 o (kL cos e ) 0 with L = 3.6 m and W = 7.92 m. (iv) Each of the two tail fins is approximated by a rectangular metal plate oriented in the y-z plane. This combined contribution (a4) is obtained from (6.15) with L = 4.32m and W = 1.44m. (v) The two engine ducts in the front are approximated by circular cavities each having a diameter a = 1.5 m. The scale model indicated that the opening of each duct is one-fourth of the complete 2 circular area, Ta. The contributions (05) of the two engine ducts is obtained from: 2 sin (2ka sine ) 5(0 ) = 0.05(ka) 2(6.16) 5 0 (2ka sin 9 ) for 0 < 0 < 84~. - o - (vi) The two exhaust ducts, located in the rear of the aircraft, are modelled by circular cavities each having a radius a = 0.5 m. Their combined contribution (a6) is obtained from: 37

2 3 2 sin (2ka sin 9 ) 06(0 ) = 2 x 0.4(ka)32 - - 2 (6.17) 6 0 (2ka sin O ) 0 for 135~ < < 180~ - o -- Note that all linear dimensions are expressed in meters and the calculated cross sections are obtained in square meters. Also note that shapes and dimensions of the scattering components are assumed such that their scattering cross-sections are polarization independent. The z-coordinates of the scattering centers of the above components are: z= 9.36 m, z2 = 0.0, = -.7.2 m4 5 + 1.08 m and Z6 =- 9.36 m. Even after identification of the various scattering components, proper care must be taken to combine them for a given aspect angle. This is because the geometry may be such that at some aspect angle parts or all of the scattering from a component may be shadowed by other(s). To avoid the complications due to shadowing effects, we have restricted ourselves to the determination of RCS in the x-z plane and proper considerations have been given in obtaining the cross section expressions given above. 6.5 Numerical Results Figures 34(a) and 34(b) show the static average, RMS and relative phase crosssections, o', a' + s and a, respectively, versus aspect angle 6 for the aircraft obtained at X = 3 and 30 cm. Of course the average cross section o' stays within the RMS bounds 0' + s at all aspect angles. Over most of the range a also stays within the RMS bounds; at some aspect angles, o moves p p out of the RMS bounds. These results are in general agreement with results discussed elsewhere [18, 19]. The dynamic cross sections are obtained for the fundamental vibration mode at w./27r = 6 hz and a wing tip half-deflection t =o 0 3 cm. 1~ 38

iwo sets of dynamic RCS have been obtained: one referred to as the tip-scattering center assumes that the scattering center of the wing is located at its tip which would experience the maximum displacement due to the induced vibration; the second set of results, referred to as the mid-wing scattering center, assumes that the scattering center of the wing is located at its center. Figures 35(a-e) and 36(a-e) show the dynamic RCS as a function of time and for selected values of the aspect angle 0. Observe that the results are shown over a complete cycle of vibrations at the dominant mode. Notice that at some aspect angles, the RCS values at X = 3 cm are lower than those at X = 30 cm; this is due to the fact that those aspect angles are located at or near the nulls in the RCS pattern at X = 3 cm. Generally, the dynamic results in Figures 35 and 36 indicate that the aircraft vibration induces some kind of fluctuation (or modulation) in its RCS. At most of the aspect angles, the total deviations in the dynamic RCS values from the corresponding static values appear to be more at X = 3 cm than those at A = 30 cm. The fluctuations appear to be large at selected aspect angles. As a function of time, the modulation in the RCS for A = 30 cm appears to occur at the frequency of vibration of the aircraft. For X = 3 cm, the modulation also contains a component of the vibrating frequency at all aspect angles; in addition, at longer aspect angles (0 = 35~, and 45~) there exist quite strong third harmonic components. The location of the scattering center of the wing at its center or tip does not appear to change the general nature of the results. Observe from Figure 35(e) that at 0 = 45~, as a function of time, the total deviation in the dynamic RCS, at A = 3 cm is about 8 dB. However, the static results shown in Figure 34(a) indicate that near 0 = 45~, the RCS varies quite strongly with 0. If it is assumed that aspect angle varies about 0 39

+ 2~ due to reasons other than the induced aircraft vibration, then careful study of Figure 34(a) near e0 45~ indicates that this may cause about 1 to 5 dB variations. This implies that under such conditions vibration-induced modulation would produce about 3 to 7 dB deviations in the dynamic RCS. Perhaps it should be mentioned that low frequency variations in the observed dynamic RCS of aircraft have been reported in [20,22]. Our results here tend to indicate that these may occur as low frequency variations in the RCS of the aircraft due to its vibration induced by air turbulence. In our scattering model we have neglected the effects of shadowing by the individual scattering components and of the incident polarization. The accuracy of the assumed model is satisfactory for the static case [18] and should be acceptable for rough estimation of the general effects in the dynamic case. Further study is required to obtain the detailed nature of the effects of aircraft vibration on its RCS. 40

VII. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY 7.1 Conclusions Three fighter aircraft have been analyzed for aeroelastic response to gusts and turbulence. The study included the effect of operating conditions on the modal frequencies and shapes, as well as determination of relative amplitude response of elastic modes. It was found that airspeed had a moderate effect on frequencies and modes for all three aircraft. Fuel and armament loads had a large effect, particularly when carried on the wings (as opposed to fuselage). The one aircraft with a swing-wing had dominant fuselage bending at the lower frequencies; these modes were changed only moderately by the wing position. Perhaps a more critical issue than the invariance of the modes is whether the modes are excited sufficiently by gusts and turbulence to allow observation. Only five percent of the atmosphere contains turbulent patches with a gust greater than 2 ft/sec. recorded at least every ten seconds. A five-mode simulation of the symmetric wing bending problem was carried out for each aircraft, using a 2 ft/sec. sharp-edged gust. Each of the aircraft responded with a total elastic wing tip deflection of 3/4-inch or less. The bulk of this response was in the first mode, and response in higher modes was small. The only situation which has any promise for identification is the fundamental (fuselage bending) mode for the Type A fighter/bomber. The frequency of this case can be mimicked by smaller fighters carrying sufficient stores. Therefore, for success, some unique characteristic of the mode shape, such as the large tail motion, needs to be exploited. 41

After identifying its dominant scattering components, a theoretical scattering center model has been obtained to calculate the RCS of a type A aircraft. Average RCS and relative phase RCS of the static aircraft have been determined as functions of the radar aspect angle, and for A = 3 and 30 cm. It has been assumed that the radar is ground-based, and the RCS calculations have been performed in a vertical plane such that the shadowing effects on RCS are minimum. Dynamic RCS of the aircraft has been obtained by assuming that the appropriate scattering centers experience vertical displacements (in time) produced by the motion of the aircraft undergoing its fundamental mode of vibration induced by air turbulence. At some selected values of aspect angles, we have determined the dynamic RCS over a complete time period of the fundamental mode. With the assumed scattering model, the dynamic RCS of the aircraft in the nose-on direction appears to be independent of the aircraft vibration in the vertical plane. In other directions (aspect angles), the RCS values appear to contain amplitude modulations at the fundamental and the third harmonic of the frequency of the fundamental mode of vibration of the aircraft. Although these modulations are generally found for both X = 30 and 3 cm, those of the latter wavelength appear significant enough to be observable. The significant finding of the study is that the motion of the aircraft induced by air turbulence seems to produce low frequency amplitude modulat-ion of its ambient RCS. From the considerations of the maximum vertical displacements due to turbulence suffered by the wings (or wing-tips) of a Type A aircraft, it appears that such modulations may be observable with a 3 cm groundbased radar system. At the completion of the present study, it is not clear 42

whether such observations could be used to identify the aircraft. Further investigation is needed for this purpose. 7.2 Recommendations The present investigation should be considered as a preliminary study of the general problem of identifying an aircraft by its RCS modulations induced by airframe vibration. Although some of the results of the present study are found to be significant from this point of view, they are not complete and well understood. Therefore, to ascertain the potentialities and practical realizability of this method of aircraft identification, the following studies are recommended. (i) Obtain the RCS vs. time for a given aircraft in flight. (ii) Obtain experimentally the RCS modulations for a model aircraft undergoing a motion simulating that of the fundamental mode of vibration. (iii) Investigate the implications of the results obtained in (i) and (ii) with regard to the identification of the aircraft. 7.3 Unresolved Points Some unresolved technical points include: (i) Should the identification be based primarily on random or deterministic concepts? In the present study, deterministic ideas have dominated. (ii) If a random approach is taken, are the newer, non-Gaussian turbulence models [23] more appropriate than the von Karman isotropic turbulence model? Although more accurate, the newer theory will probably not be worth the computational effort. (iii) How much effort does the longitudinal rigid body pitching mode have? The so-called short longitudinal mode has frequencies of the order of one hertz and is felt not to couple into the problem. /. A

(iv) Will the active control systems of the future couple with gust and turbulence response? Both the Rockwell B-l and the latest versions of the Lockheed 1011 have active systems which suppress elastic modes but may introduce frequencies peculiar to the control system. 7.4 Acknowledgements The authors have been supported in this study by many suggestions from Mr. John Lennon (RADC/EEC) and Professor Thomas Senior. Aircraft data were supplied by Mr. Walter Dunn (ASD/ENFSR) and FACES program assistance by Mr. Sam Pollock (AFFDL/FBRC) and by Mr. M. A. Ferman (McDonnell Aircraft Company). This help is gratefully acknowledged. 44

VIII. REFERENCES [1] Ferman, Martin A. (1975), "An Extension of the Rapid Method for Flutter Clearance of Aircraft with External Stores," vol. I, Theory and Application, McDonnell Aircraft Company, Air Force Flight Dynamics Laboratory Technical Report AFFDL-TR-75-101, vol. I, November. [2] Unger, Walter H. (1975), "...vol. II, User's Manual for FACES Computer Program, AFFDL-TR-75-101, November. [3] Wells, J. R. (1975), "... vol. III, Programmers' Manual for FACES Computer Program, AFFDL-TR-75-101, November. [4] Houbolt, J. C. (1973), "Atmospheric Turbulence," Dryden Research Lecture, AIAA Journal, v. 11:4, pp. 421-437, April. [5] Hardy, K. R. and Ottersten, H. (1969), "Radar Investigations of Convective Patterns in the Clear Atmosphere," Journal of Atmospheric Sciences, 26, pp. 666-672, July. [6] Fujimori, Y. and Lin, Y. K. (1973), "Analysis of Airplane Response to Nonstationary Atmospheric Turbulence Including Wing Bending Flexibility," AIAA Journal, 11:3, pp. 334-339, March. [7] Fujimori, Yoshinori and Lin, Y. K. (1973), "Analysis of Airplane Response to Nonstationary Turbulence Including Wing Bending Flexibility. Part II," AIAA Journal, 11:9, pp. 1343-1345, September. [8] Coupry, G. (1971), "Critical Analysis of the Methods Used for Predicting the Response of Large Flexible Aircraft to Continuous Atmospheric Turbulence," AIAA Paper No. 71-342, April. [9] Roskam, Jan. (1971), Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes. Published by the author, The University of Kansas, Lawrence, Kansas, 3.2-3.3. [10] Fung, Y. C. (1955), The Theory of Aeroelasticity, John Wiley & Sons, Inc., New York, pp. 280-282. [11] Bisplinghoff, R. L., Ashley, H. and Hoffman, R. L. (1955), Aeroelasticity, Addison-Wesley, Reading, Massachusetts. [12] Hamming, R. W. (1973), Numerical Methods for Scientists and Engineers, McGraw-Hill Book Company, Hightstown, New Jersey, pp. 375-377. [13] Bathe, K. J. and Wilson, E. L. (1975), Numerical Methods in Finite Element Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, pp. 322-324. [14] Swerling, P. (1954), Probability of Detection for Fluctuating Targets, RAND Corporation Report, RM-1217, March 17. [15] Swerling, P. (1968), Radar Target Signatures, Intensive Lecture Series, Technology Service Corporation, Santa Monica, CA, August 26-30. 45

[16] Marcum, J. I. and P. Swerling (1960), "Studies of Target Detection by Pulsed Radar," IRE Trans., vol. IT-6:2, pp. 59-267, April. [17] Nathanson, F. E. (1969), Radar Design Principles, McGraw-Hill Book Co., Hightstown, New Jersey, Chapter 5. [18] Crispin, J. W. and Siegel, K. M. (1968), Methods of Radar Cross-Section Analysis, Academic Press, New York, New York, Chapters 9 and 10. [19] Crispin, J. W., Jr. and Maffett, A. L. (1965), "Radar Cross-Section Estimation for Complex Shapes," Proc. IEEE, 53:8, pp. 972-982, August. [20] Skolnik, M. I. (1970), Radar Handbook, McGraw-Hill Book Company, Hightstown, New Jersey, pp. 28-3 to 28-5. [21] Crispin, J. W., Jr. and Maffett, A. L., (1965), "Radar Cross-Section Estimation for Simple Shapes," Proc. IEEE, 53:8, pp. 833-848. [22] Olin, I. D. and Queen, F. D. (1965), "Dyf:azci Measurement of Radar Cross-Sections," Proc. IEEE, 53:8, pp. 954-961. [23] Pi, W. S. and Hwang, Chintsun. (1978), "A Non-Gaussian Gust Model for Aircraft Response Analysis," AIAA Journal, 16:7, pp. 641-643, July. 46

IX. TABLES Table 1 Aircraft Weights The airplane cases studied follow. In all cases, additional loading is simulated by inertial effects alone. Type A: 2 different wing-sweep configurations, 3 internally-loaded cases A) 16 deg. 1. e. sweep 1 —1: dry airplane ('light') gross weight = 44,507 lb. 1 —2: dry wing, 23,327 lb. fuselage fuel ('medium') gross weight = 71,834 lb. 1 —3: 5,468 lb. wing fuel, 23,327 lb. fuselage fuel ('heavy') gross weight = 77,302 lb. B) 72.5 deg. 1.e. sweep 1 —4: dry airplane ('light') gross weight = 44,507 lb. 1 —5: dry wing, 23,327 lb. fuselage fuel ('medium') gross weight = 71,834 lb. 1 —6: 5,468 lb. wing fuel, 27,327 lb. fuselage fuel ('heavy') gross weight: 77,302 lb. Type B: 3 externally-loaded cases 4 —1: clean airplane, unloaded pylons ('light') gross weight = 37,704 lb. 4 —2: 2 loaded pylons per semi-span ('medium') total of 4 loaded I/B pylons per airplane (14 M117GP bombs) gross weight = 49,068 lb. 4 —3: loaded pylons per semi-span ('heavy') total CF 4 loaded I/B and 4 loaded 0/B pylons per airplane (I/B: 14 M117GP bombs) plus (0/B: 2 MK81 bombs and 2 LAU 32 A/A FFAR rocket gross weight = 51,752 lb. Type C: 3 externally-loaded cases 5 —1: clean airplane, all stations unloaded ('light') gross weight = 15,265 lb. 5 —2: I/B and tip stations loaded ('medium') I/B pylon: 50% 150 G. fuel tank Tip station: AIM-98 'sidewinder' missile & launch gross weight = 17,258 lb. 5 —3: 0/B ANC tip stations loaded ('heavy') I/B pylon: full 275 G. fuel tank O/B pylon: BLU-27/B(F) tip station: AIM-98 'sidewinder' missile & launch gross weight = 21,908 lb. 47

X. FIGURES 48

109720 109722 1072 109 I. 40 30 o 069909 '239706 079907 079907 0 099815 q p p 578116 > ------ o --- —----- - 329 507 N 14 4 -trl u 1) O v) O pc 20 '224984 Mixed 513280 568209. -. I I Wing bending and torsion.. 73681 - Wing bending and torsion, v - -,. -:" w,,11 w........ I 411690 Fuselage bending 341693 1 o0 ( Fuselage bending 250397 240397 a a I I I 0 I I If W SMIN~m / r% P. - 200 400 ouu U0J Equivalent airspeed at sea level, V, knots Fig. 1. Modal frequencies of aircraft type A in flight. Weight = 44, 507 lb. (Dry airplane, 16 1. e. sweep, symmetric modes.)

40 069906 049906 069906 04990 30 573276 329 503 561781 0 -Jo 0 - a 189803 57 58 58 C)PI~,, N.. 418241 Kp~ Is_-, 20 756318 Wing bending and torsion 6 0 1 A 355179 Fuslag beding 1 C). 71r —_- -- - ~- -:- ~ —~- - r -" -- - - - --- T — 3 55179 Fuselage bending 124489 -uw- - m -. —I -421V689 - 10 Fuselage bending 41.198, 200298 Fuselage bending 240297 I I I I I ~'~A ~J~r~%an*ap~i~lsa~sr~~h ~ ~ m~11~~L~-~~-i~~ —r~~s~yi~a -;ul~L; ~BI~l-rR 1~g~~p~fWI~Ba~Y -A -— a ar~ 200 400 6 0f. 800 (Ji pivalelit airspeed at sea level, V, knoi >'.LJai"~ f ~t, type A in 'light, Weight:71, 4 lb. (-Dry wing, full fuselage fual J e &W;ap, syr nmetrc-IK modes. N

40 30 059907 109907 -00-0 533279 494078 p -c - _ ~ ----- un 1 59905 -, _-___ 049820 586056 - -- -,..~..-;........ 0 — 7-.. Ol N 0):j cr, a) 1 -4 - 20 10 25942 5 n / 471187 Fuselage bending 36b49U - - -1 db 0 -b C - - - ==lI D ~ ~ -- _r~-0 -855114 Wing bending and torsion 776215 * * *. a - 2 _ - 521883 Fuselage bending 492284 210298 Fuselage bending 250297 a I I I I I I I i III..... ---. a 60 80 0 0 200 400 600 800 Equivalent airspeed at sea level, V, knots Fig. 3. Modal frequencies of aircraft type A in flight. Weight = 77, 302 lb. (Full fuel load, 16 1. e. sweep, symmetric modes.)

i I Burn off Fuselage fuel 40 109722 No_ Burn off Wing fuel 04990 6 - 561781 189803 418241.6079 13 T099815 N ti4 30 20 -. 1% 329507 513280 Wing bending and torsion 109907 494078 049820 259425 362490 77621 5 492284 250297 I. I 568 209~ ""~~~~~~ --- —~ -- - 7 -- ---------- Fuselage bending Fuselage bending ----- 124489,! 10 124489 7I 411989 240297 8 - 2440397 0 5p 00c Fuselage bending 10, 000 1 5, 000 20,000 2 I] I i G9,i. i I 30., 000 Winr.g dry t Full fuel. load Fiuel load,, lb. 500 knots -- 575 mph,:i, i...:g fuel l.oad for a-rcraft type A at Y-0 knots. (16~ I.e. sweep, symmetric V " K CiK.

109720 i69906 0 5990' 69909 573276 533 329503 3 0 - 1 30239706 329__ 15C;. ---^ --- —---------------------------------— 8 ---- 58( 578116 7 56318 ^ 20 224984 Wing bending and torsion 47 736810 Fuselage bending 3551 l C i, 42 689 I 411690 Fuselage bending 10 ': " 'T __________' ----" --- —— ^3?) — 2 250397 Fuselage bending 30, 000 209000 0 o10, 000 Fuel load, W, lb. Fig. 5. Ground vibration frequencies for aircraft type A with varying fuel load. (160 1. e. sweep.) Fig. 5. Ground vibration 11eque4 I - 1z. 60 5(,5114 10298

293688 40 'U IN C 239705 805329 293689 0 0 -a - f 269604 - % 81522 — 81 5228 --- - -- - c- A -- ~ 30 Irl 0~ Q)!j k 538 503 ) --- —— ~-0....... —/ - - - 528 50 5 ~DI --- -- ---- p 0 481886 Fuselage bending 462086 ---- -,. -- --- -- ~~ - — a 864031 Wing bending - p - - - - " 353'138 0 I O m -l -Go-IL ~ D1DC ~I ~ L~_ - m m C I-yp — -M ----I —.661175 Wing bending and fuselage bending 621078 250497 Fuselage bending 21( )498 0 "00 200 I I a I I — b-~IIF IYyc-Lgyl --- — 1 ill 1Aige ~ -9 1 I --— 9-rh~ — 1 UI 300 400 500 600 700 800 Airspeed, V knots eq4 0 -vfte~ A in fl-ght. Wei-ght 44, 5&7' ~tb, (Dr,, air-plane, 72., 5 ie _ 1gI - C. -~~~5 vet:. &<w<I

40 249616 279601 db Ah db All'. ap - 292293 ----- --— o 282194 --------------- 30 825513 0 0 - He 795915 N r( 0 O Q cr( 0 -o — 159 ---5-o 159527 30 633669 Wing bending and fuselage bending a RP - -4m 4p -- 654065 O 903427 893627 Wing bending C 0 I -- 10 low low w - 691471 Wing bending and fuselage bending 711369 0 o{ 190298 Fuselage bending 180298 I I I I I I I I * 5 U a l 0 100 200 300 400 Airspeed, V, knots eq 500 600 7(UU tUU Fig. 7. Modal frequencies of aircraft type A in flight. Weight = 71, 834 lb. (Drying, full fuselage fuel = 23, 327 lb, 72. 5 1. e. sweep, symmetric modes.)

40 339220 329221......... --- - __ o _....o 303987 30 -930935 940834 ^ 139814 189809 20 2 482584 Fuselage bending 50288 q 883531 Wing bending 883533 1- ~ — f-f --- —-ftI~ ------ e-PC-~~II —~ ---^^.-:iC)L -— ~4-~ ---ft-~ ---~ 711669 Wing bending and fuselage bending 791659 180298 Fuselage bending i 70298 100 200 300 400 500 600 700 800 A.ir -peed, V, knots eq:ig. s. I;al fr. f -Iquerc.s -of.ircr-ft t iYpe A in fligWbt. 'Weight = 77, ^-: Ib. (Fully fueled, 72.5 1. e s.,,eep, symre: tri c - ordes ) I

40' 30 4 -a) 4-4 U a) a) 04 -cr' (1 w4 20 10 Fuel load, W, LD. % Wing dry Fu Fig. 9. Modal freencies for aircraft type A with varying fuel at00 knot (72 e sweep symmetric modes.)

40 I I 8249 I292 616 293 >513 2 30 I 30 JUl.X 339220 303987 Q30935 1 39,.214 482584 883531 711669 180298,-f.14 1+4 m a) -4 u r (1) 'iI cr 0);_1 '4-; 1-1 N, 0 0 C- I 20 10 538503 481886 I __j Fusela e bending I,633669 269 m 9 3 6- - 864031 Wing bending......... I -~~~~~~~- -..- s y 661175 Wing bending and fuselage bending %049 7 Fuselage bending I! 68936271 --- 4 W 691471 ^ - -,,-_-..- - 190298 a f I 10, 00( 2, 000 30, 000 Fuel load, W, 1b. 'g,. i <, (;,; - 'or aircraft Aype A with varyi~g-, fuel load. (72. 1. e. sweep,

235779, 175681 2 3 5 — 1 75 40 ~ 379307 409108 - --- > db k. 377851 358146 N 30 ^ >a 0 - 20 ^4-1 ( 149904 > _ 379305 337557 Wing torsion 368245 627807 Wing and torsion 5980 04 627807 Wing bending and torsion 598004 ( A/iT vAd 74 5144 645r53 5 53 841 86491 5 864912 Wing bending I I I I I I I * * la a a a 0 O ) 200 400 600 800 Equivalent airspeed, V, knots eq Fig. 11. Modal frequencies of aircraft type B in flight. Weight - 37, 704 lb. fueled, symmetric modes.) (No pylons, partially

40 30 20 ( 10 0 ( 102796 112596 Ak 174985 114986 0 0 - - - -, ~ — - FPI O 488708 lw- 508607. -----.-. 1T63294 ~223292 W- -Wing bending and torsion — 657603 62780 Mixed 6864 36 -6 FT... 923714 Wing bending 873932 844 332 874423 Wing bending 0 I I I I I I I _qyt;6%~~gl;.llAjyrarW-Ur-.Y ---.C a/-~I. uc~~-pi --- —-— ~-~ --- —~ —~L — 7-sracsacCI -Ai.-P-JFanirpl C - pPI-- 318PiPllFI -Bwa I)-s s BY- II - I C 0 200 400 600 800 E~quivalent airspeed, V, knots eq Fig. 123. NIodal frequencies of aircraft type B in flight. Weight = 49, 068 lb. (Four pylons per wing 'wth'# to lE(R racsF, i, 364 Ib. armament, syrrmetric modes.)

40 30 045286.. -065583 u 389114 -------------- O 20 103095 602 329501 I v0 ---------— O | 507838 Mixed 50 -- 1778 10 I Wing nding and torsion 8450 23 Mxx ~ 795331 864621 Wing bending 0 --------- * ---- ' ---— MI. ~ I,- I - ---- r --- 0 200 4 Equivalent airspeed, V, knots eq Fig. 13. Modal frequencies of aircraft type B in flight. Weight 51, 752 lb. (Four pylons with tM MER per wing, 14, 048 lb. armament, symmetric modes.) O10

40 30 10 4 inb~oard pylon s ,- I- 4- r, ri n i-, +- c, IQ%7- ri-, -rn i- f- r I r, m o,-11, f- s. I

40 1022796 w 4-i 30 20 I11 04E,286 389114 063 19 149904 337 557 84502 3 864621I 0 W, 00lb. r e t. (S y my-m e tric m o e ) Fig. 15 Ground vibratiofl frequencies for aircrf ye$wt ayn ra

60 c I,. I 1,. to r -iorn 269606 r --- — G 0~L-Lo --- U~~ 11~I~ I-,~ I ----- 14W 50 129902 wing torason. 'Ok-339406 - - ----n r. --— i -- A I - I 1 277462 wing torsion 279130 — 2 --- — p 401'm wing bending and torsion 73680?' 4.4 ON X — II,.+>1 301in 931 534 wing bending 80245t ' U _ __-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ __ _ _ _ _ _ _ _ _ _ _ 4r U-7 - 20 775237 933705 Ipb - P wing bending 8 bd46n 8 wing berd lmr — - 5;.111, Flutt Mode I-W 10 - 2o0-496 ---f l pgebending -270496 fuselage bending -— oo 220497 L. _I I a a a:.~J-suClhP-uln*-~;ad, - W I I,~ag BL I~ A I a 0 200 I I I 400 0U0 800 Equivalent airspeed at sea level, V, knots e q c1& A r- o. eic for aircraft type C in flight. Weightl, 15, 265 lb. Internal fuel only (liiJihh).

40 30972501 wing bending 972601 30 532681 fuselage bending 502782 U o ' - ------------------- 20 972010 wing bending 972209 ) -— 0 --- 903229 wing bending 883432 286471 wing torsion and fuselage bending 297658 10 725641 73 12 69 5251 wing bending and torsions 904208 746706 667410 wing bending and torsion Flutter in Mode (g=0. 03) 0 I II II.I-I..I,.. l 0 200 400 600 800 Equivalent airspeed at sea level, V, knots eq Fig. 11 Modal frequencies for aircraft type C in flight. Weight- 17, 258 lb. (Symmetric modes.)

20 1 5' N '4-' I i a 943308 0 a - - 0 0 0 - 342391 fuselage bending OM - ) ~ —.0 - 332392 wing bending I N i 943308 2 59705 wing torsion 379209 OL -.. lw. -- ~ 10 462286 fuselage bending 442188 - - 694258 nmixed 584965 k L I - Ak - & INk -AM -- W- a - - - a It -0 -4&- -8 - - - 83219 wing bending 3_5___6 N — — p --- ------ am n 17 3 It I fn OQ k f'7Cm -- r s Yl-rl r - v Z 1 U Wig UDIlnL1gi 7 c f 5830 wng torsion 139238 5 2 8 03 0 wing torsion 1 392 38 Flutter in 1st Mode (g=O. 03) 0 I ).200 w a-,.K1<42 -ff 0.X a I I I A-Wxm- 94-ve-MIM-10 I ( 400 I 600 800 Equivalent airspeed, V, knots eq -:1 -r- -1.., -( P, r - -1.-.. I, - -. I I, !-. r,... -,; - ft t Tr, n Cr in flight. Weight- 21. 908 lb. (Symmetric modes.)

60o-! 269606 Wing to:;ion 501 - 4 339406 279130 736802 Wing torsion Wing torsion Wing bending and torsion 40 4 N '4i-i >1 u 0' QU cr Q) IL4 301 802455 Wing bending 874615 Wing bend. % 972601 Wing bending V 502782 Fuselage bending > 972209 Wing bending ~ 883432 Wing bending 2 0 894605 Wing bend. 220497 Fus. bend. 10 297658 725641 904208 746706 Wing torsion Mixed Wing bending Wing bending and torsion %943308 Wing bending V 332392 Fuselage bendin ~ 379204 Wing torsion 422188 Fuselage bendirio O 584965 Mixed A 943506 Wing bending D 981707 Wing bending o 139238 Wing torsion I I I a I I I 0 Is I - I I p - L - - zls - - - L 1 I B - P- - 0 1000 200C 3000 4000 5 Armament weight on pylons, lb. 000 6000 7000 8000 Fig. 19 Modal frequencies of airplane type C in flight at 500 knots. (Symmetric modes.)

601Om 2 239705 50 - 1 " CQar I L ) 7 7V L?77462 815902 40 00 O L. >, cr l^ 30o 931534 775237 933705 20 ( 97250] V 532681 0> 972010 9 903229 286471 9 695251 a 73671-2 o 667410 10 0 ) 270496 <, 943308 V 342391 o 259705 a 462286 o 694258 o 835219 972110 0528030 I I I I I I I I A AI 1000 2000 3000 4000 5000 6000 7000 8000 A:i iLarnient weight on pylons, lb. PFi. 20 Ground vibration frequencies for aircraft type C with varying fuel and armament load.

17 5681 "Optimal" mode tracking RMS error - 22.8 RMS error - 18. 3 40 112596 tN Or sq.1 4 - 30 20 065583 438914 103095 329501 508516 617718 10 318051 795331 1 r nr i 0 0 5,000 10,000 l, UUU Armament weight, W, lb. Fig. 21 Automated mode tracking attempt for aircraft type B at 500 knots. (Symmetric modes. A rework of data in Figure 14.)

69606 Wing torsior) Wing tobrsion 2 Wing bend. torsion OPTIMAL" mode trackiing RMS error = Z3.1.\ ~ si~"PlA~ oetakn 30 972601 Wing bending RMS error - 20.2 o 1 802455 Wi benrg / 50332392 Fuslage be 20497 Fbus. ebend76 nd5 Wing torsi Wing tors 102 422188 Fuselage bei o 20 Wing Wing bend. 746706 Wing bending & toro 943506 Wing bendinr bending 10 2c 422 1878 Fuselage bWing bend. 746706 Wing bending & torsion 943506 Wing bendi981707 Wing bendini 139238 Wing torsior 1, -7,d 3_ y II r"r1J-n 0 L.~ 0 1000 2000 3000 4000 5000 6000 7000 8000 Armament weight on pylons, lb. Fig. Z2 Modhi frequencies of airplane type C in flight at 500 knots. (Mode tracking "experiment" wit-t frequency data. Synnmmetric modes.)

60 C(REF) B(RE A(RE F) B (pa.tiaill-y a cr."5ed) C (Partially1 armed) A Pc.. i, fuelied-I 50 40 (Fully armed) A! (FtullG; ft eled ) C (Fully J 30. f 1 0 0 10, 000 20, 000 30, 000 40, 000 50, 000 60, 000 70, 000 8 Armament weight, W, lb. Fig. 23. Composite relation between modal frequencies and total aircraft weight at 500 knots. (Reference aircraft have no external stores.) (Symmetric modes.) 000

Figure 24(a). Fundamental mode of aircraft type A with wing fully forward (16~ 1.e. sweep). 494 knots at sea level. Medium weight = 71,834 lb. Verticat displacement of wing. f - 5.98 hz --- - - r~~~ -L. + u in 4mA I Mr &A on_& --- L.Sh o md l-L - - A -A — A"t ^^r m 0. 100. 150. 200. 250. 300. 350. 400. LLIJ Ld UI N (D o~ STI I, IN, A MEDM, WING Z-D, 493.6 KT MD 1 M -- W --- - -. FT's a c

Figure 24(b). (cont.) Torsional rotation of wing. I 0 a:, 0. ft CD z 0m 1 0N 100.1 300.1 400., Fy MEI1 STEN7 IN7 A MEDMFWIN6 *-0. 1~

~_II __ ' Figure 24(c). (cont.) Vertical displacement of fuselage. LLi Cr) U 40. 20.' 0.S STI,INLET I EXHAUST I DUD a1 6K y -1 IN 200A MI

Figure 25(a). Fundamental mode of aircraft type A with wing fully } swept (72.5~ I.e. sweep). 498 knots at sea level. I edium weight = 71,834 lb. Vertical displacement [ of wing. fl = 6.03 hz. *-, ^-&- -r "~ ~~ -1 — — + ---4 50. 100. 150. 200. 250. 300. 350. 400. ILJ T i Nr A MESWWING Z-D,498.4KTrMDl LL CQ 4. N Z3 -12.

Figure.125(b). Fiur 2(b. (cont%-.) Torsional rotation of wing. C0CD1 z% II 0 2 - onij 0a.0 SI~ — +- i i UI ---.0 00" 11" 0 0 I? A s F I 0i -IMD 1 -100 11

i Figure 25 (c). (cont.) Verti( i cal displacement of fuselage. LJ LL 1 LJ (D L 40. + -L --- i jLL i -i INLET I l L I I I,. I I I I I a *i,..Lti tr EXHAUST 1000..4KT, MD1 0....- -L - - -. - -... - 9 a a S STI,7 INr 200. A XT-I a V I r I -, Ia I I I —T 00. 6l. M W FUS, Z-D, 4 I 91 800 498 -20.

--- —CC ---CI ---CIC — -----— ~ --- —-L __ __ __ Figure 26(a). Fundamental mode of aircraft type B. 533.5 knots at sea level. Medium weight = 49,068 lb. Vertical displacement of wing. f = 6. 70 hz. I- X ULJ LLU L- 20.I (D 10." H PYLON I i PYLON 3 1? 0. I I L pi.LI1 o ---+200. 250. 300.,WING W7. 433.5KTr MD1 rr `~t% -10.

i Figure 26 (b). (cont.) I Torsional rotation of wing. Ut H 0~ CD z 1. f 1 2 0.0 s1 I,,.. A i I?; I N? t6B ME~?W I N 0 3T, 4; %TD 1K

___ __ __ ___ ' Figure 26(c). (cont.) Vertical displacement of fuselage. _ ____,I I INLET I EXHAUST I I I I 0. 100. -— o.00. 700. -433 433.5KTr MD 1 LLJ LU LL0% I N V) Z-, IN, B MEDM, -4. -8. -10. -12.

2: 0 F-C) S Q) CO v-i4 a -44 ' —4 0 H0-) S (N N 2: 0 2J-I a C0 (N v-i4 a C0 C0 S.. LUL () 84b z %.. I S. ' 0 a 114, I S iliii CQZ 9NIM I Figure 27(a). Fundamental mode of aircraft type C. sea level. Medium weight = 17,258 lb. displacement of wing. f1 7. 46 hz. 483 knots at Vertical

z 0 - "-.4 Ii-4 a rn0 6A-i-i HQC S a N '-4 a a Lii a GIVH'(LO~I 9NIMA Figure 27(b). (cont.) Torsional rotation of wing. 82

I X LJ 1I I I I I9 it I /~ J* -- LL z 6 0 IZ 0 0 I l33'aO-z 3sn] Figure 27(c). (cont.) Vertical displacement of fuselage. 83

14 12 sea level 10 8 / 40,000 ft. altitud 4) O U 0 2 4 6 8 10 Elapsed time, t, sec. Fig. 28. Sharp-edged gust response for rigid type B aircraft. Gust vertical velocity = 2 ft/sec. Aircraft weight = 54, 611 lb. e 84

a u ui (n NS,, a LL 0 a CY) 4*.039: Cf) Fu 0 -i uj In a V-4 r"I a u Lli co Li a a a CD co (10:DI CD 0 LLJ 4 Z: -4 b*.:D C) a 0 a %.-dp 0 C5 6 1 lll-) 3 v -1 C4,9 1 a a 0 Jli —9NIA C) a C) Figure 29. Elastic response to sharp-edged gust., air f t ype A. 85

a LUi (I) a HLL N C~) a N 0 a-Li (a, a Lf) u L U '-4 (n LUj '" i-4 D II C [ii H (D LO) a 0 6 a C C OL a 0 6 iNIW9OV-ldSIO dIlr9NIM Figure 30. Elastic response to sharp-edged gust, aircraft type B. 86

a LUI (JO) NS. LL N 0 -J CD 0 UY) 0 (N LOU zsu C) a U) 0 aS 0 - CI 0 0 ~N2J4WDOV-IdS I dJli-9NIA Figure 31. Elastic response to sharp-.edged gust., aircraft type C. 87

H. LI) tr%) PEAK GUST VELOCITY 2 FT/SEC f-f H. C!q LA) H. O00 rt Id 0* 0_ (0 H. 0 CF2 (0 C) (0 to% z I 0.1000+ 0.001ef e0 0o0s+ C a A 000001i'= et 2 Iv e, 4, ----- G-" -v so. LOWER FREQIJENCY.ILIP4!T ON POWER SPEC~TRUM CHZJ RIGiD,-ODY PLUNGING RESPONSE rO CONTINUOUS TUR~BULENCE

x Figure 33. Aircraft coordinate system used for RS calculation Figure 33. Aircraft coordinate system used for RCS calculation 89

4~CD o 1 -1i0 N) CDr w C~) o<< zo0 t-HLOL C(2j, 6) 6 (El C 'W Os9) 90

60. 50. 40. WAVE-LENGTH = 30.0 CM. 6 Or) _Jr — UJ a c21~ " it 0 0 LJ (r) O L 30. 20. 10. o. -1 0. 50. 100, 200.s VIEWING-ANGLE CDEG. 3 Figure 34(b). STAT I C RADAR-SCATTER I NG CROSS-SECTION

AIRPLANE TYPE 'A' 97. 8.7.' STATIC. DYNAMIC 30.0 CM VIEWING ANGLE = 5 DEG. 61 5. tbJ -J Ui03 ma UlJ cf) D,. 4. 3.0 CM ovn! & U T A^. INTINA IL -STATIC 2 - I I — I- IO0. 0.02 0.04 O. c 0.08 O010 0.12 0.14 0. 16.0 TIME CSEC] OVER ONE VIBRATION CYCLE DYNA I C RADAR-SCATTER ING CROSS-SECTION FiL uIrce " (a)

1. AIRPLANE TYPE 'A' VIEWING ANGLE = 15 DEG. 0. 3.0 CM (f) r-%.LJ a ui Z: s-a IL) O) 00W LLJQ.J 0.. J........_ STATIC — 0.02.04 0.06 - 0.10.1- 0.4 0-6 ---3 0 02 a. 04 0. 06 0 08 O. 10 a 12 On 14 Om 16 -0. -1. -1. 30.0 CM TIME CSEC) OVER ONE VIBRATION CYCLE Figur 35(b). DYNAMIC RADAR-SCATTER I N CROSS-SECTION

I AIRPLANE TYPE 'A' VIEWING ANGLE - 25 DEG. V) rLJ a 0co O ~%. 2.5& 2.0! 1.5 -1.0 08.5 - ' Ca - __- -_ -...-.STATIC -— DYNYAMIC 30.0 CM 3.0 CM.. —. - ---- - < — STATIC d DDYNAMIC 0a I - -;-4-^ --- —~-"h --- - -— +-~-( ----.-i ---- — I O0 O0.02 0.04 0.06 0. 08 0.10 0.12 0.14 0.16 TIME CSEC) OVER ONE VIBRATION CYCLE,.~, )q. J\I",'A, h C RAf R -SCATTER I NG CROSS-SECTION

3. AIRPLANE TYPE 'A' VIEWING ANGLE a 35 DEG. 2. ) OC uiLJ Q<-~ 2. STATIC -— C30.0 CM) STATIC -— C3. O CM) 2. 2.2I --- i —i ---i --- — - - a i —I —ai — 0.0 002 0.04 0.06 008 0.10 0.12 0.14 0.6 0.0 0.02 0.04 0.06 0O. 0 0.10 0.12 0.14 O. 16 TIME CSEC] OVER ONE VIBRATION CYCLE DYNAMIC RADAR-SCATTERINO CROSS-SECTION Figure 35(d).

16. AIRPLANE TYPE 'A' VIEWING ANGLE = 45 DEG. 0 CM) 14. 12..-J LLJ E 03 L.) C Q-~. u3 La 10. N0 0' 8.-a 0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 TIME (SEC) OVER ONE VIBRATION CYCLE DY.I- T C' RADAR-SCATTER I NG CROSS-SECT I ON Fiasirp i fpc^

9. AIRPLANE TYPE 'A' VIEWING ANGLE a 5 DEG. MID-WING SCATTERING CENTRE 8. 7. 6. STATIC, DYNAMIC 30.0 CM,,O s0 () d"'.J S ) C3 l o 4 * 3.0 CM DYNAMII 3.' 3. -- --- --- --- - - -- --- - --- - --— STAT I C,. 0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 TIME CSEC OVER ONE VIBRATION CYCLE DYNAMIC RADAR-SCATTER ING CROSS-SECTION c Figure 36(a).

i AIRPLANE TYPE 'A' VIEWING ANGLE w 15 DEG. flI-0o.".VING SCATTERING CENTRE 1.1 0. 3. 0 CM.-J a uicr) M S 0. c I- - a I IJ 0. 02.0 OoC O6.C 8 010. a12 0. 14 0. 16 - 0 -.l.. 0 - -* — -a- - -- -- -STATI C 30.0 CM DYNAMIC 4.1' 'DYNAMIIC TIMlE OVER CSEC) ONE VIBRATION CYCLE.1 1"Y'NAtil I.. '5 1; . RAFJAR-S CATTER I NO RSSETO #r..-.ROS(7 ---SECT I ON

- - jp..q- - - -- - -— WArMd=Z-S — _ - _ _ —'ar - - - - STDYNAMTIC AIRPLANE TYPE 'A' VIEWING ANGLE " 25 DEG. MID-WING SCATTERING CENTRE 30.0 CM 2.51 2. 0 1.5t en) LLJ E C] C) O Jr co 0C0L LUJO' 1 a 0.0 0.( 3.0 CM. —. --- - -. ----. STATIC -- DYNAMIC -- --.I -- —.... -— 1 -- -I A -- I D 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 TIME OVER CSEC) ONE VIBRATION CYCLE Figure.36(c). DYNAM I C RADAR-SCATTERING CROSS-SECTION

I f t AIRPLANE TYPE 'A' VIEWING ANGLE * 35 DEG. MID-WING SCATTERING CENTR,.-J a LLJ Z or: 5- a oc O LLJ cr 2. 2. ~ Q —STATI C (30 CM) -— STATIC C(3 CM) C 0 C30 CM) -DYNAMIC ( 3 CM) 0. 0 0n.02 0a.04 0n.06 Oa OC2 01 0 0. 12 0. 14 0. 16 OVER ONE VIBRATION CYCLE RAUAP-,-S-CATTERlN6 CRO""~3SECTION...,, I U Y ill\',Il - If -'I. g u i- t' — ) t "I l'- j . i - %.I

16. AIRPLANE TYPE 'A' VIEWING ANGLE a 45 DEG. MID-WING SCATTERING CENTRE 14. 12. 0 1-*j UV) LLJ a in LI W 0Ld0 10. 8.40 0.0 0.02 0.04 0.06 O0.8 0.10 0.12 0.14 0.16 TIME CSEC] OVER ONE VIBRATION CYCLE Figure 36(e). DYNAMIC RADAR-SCATTER I NG CROSS-SECT I ON

APPENDIX BILIGA- '-"lA' I 0 7.

-,, 'A' -, y - " " 0 C, Z A 1? ' "r, 1 *,, -0 -L. -0 - - -,. i I 14 J N- l!ITR. Tf 0? IC I GAN STUDY F`R U. S. AIl LO CE lEERENCES PAE FOR: 1) ATMOSPHERIC TURBULENCE 2) METHODS FOR CALCULATING AIRCRAFT RSESONSE TO TU2RBULENCE 3) VIBRATION CHARACTERISTICS OF SPECIFIC AIRCRAFT SUCH %S F4, F-1 )4 F-1 11 4) EFFECTS OF AGEING ON VIBRATION PROPERTIES OF AIRCRAFT W. J. ANDERSON SANJAY CORREA 10 OCTOBER 1977 ADAMS, M.S. AND GRANTHAM, W.D.,"ANALYTICAL STUDY OF EFFECTS OF SEVERE TURBULENCE ON FLIGHT MOTIONS OF A TYPICAL SUBSONIC JETTRANSPORT AIRPLANE," NATIONAL AERONAUTICS AND SPACE ADMINISTRATI^'N. LANGLEY RESEARCH CENTER, LANGLEY STATION, VA., REPT NO: NAS A-TN-D-5573, L-5990, DEC 69. ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT, "EFFECTS OF SURFACE WINDS AND GUSTS ON AIRCRAFT DESIGN AND OPERATION," REPT. NO: AGARD-R-626, NOV. 1974 ** THE THIRD PAPER ON WIND SHEAR MAY BE USEFUL FOR RADAP i.D. AHARRAH, R. C.,"MANEUVERABILITY AND GUST RESPONSE PROBLEMS ASSOCIATED WITH LOW-ALTITUDE, HIGH-SPEED FLIGHT," ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT. PARIS (FRANCE)., REPT NO: AGARD-556, OCT 67. AIKEN, WILLIAM S. JR AND LEAN, D., "FLIGHT IN TURBULENCE," ADVISORF GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT PARIS (FRANCE), REPT NO: AGARDB-CP-140 NOV 73 "AIRPLANE STRENGTH AND RIGIDITY-FLIGHT LOADS," MILITARY SPECIFICATION MIL-A-8861, MAY 18, 1960. AERONAUTICAL STANDARDS GROUP. ALBANO, E. AND RODDEN, W.P., "A DOUBLET LATTICE METHOD FOR CALCULATING LIFT DISTRIBUTIONS ON OSCILLATING SURFACES IN SUBSONIC FLOWS," AIAA JOURNAL, VOL. 7, NO. 11, NOV. 1969, P. 2192. ANDREWS, W. H., ROBINSON, G.H. AND LARSON, RP. R.,"EXPLORATORY FLIGHT INVESTIGATION OF AIRCRAFT RESPONSE TO THE WING VOPTEX WAKE GENERATEr PY JET TRANSPORT AIRCRAFT, NATIONAL AERONAUTICS AND SPACE ADMINISTRATION. FLIGHT RESEARCH CENTER, EDWARDS, CALIF., REPT NO: NASA-TN-D-6655, H-671, MAR 72. ANGELINI, JEANs,"ESURE DE LA TURBULENCE ATMOSPHERIQUE A TRES BASSE ALTITUDE ET GRANDE VITESSES (MEASURE OF ATMOSPHERIC TUPBULENCE AT VERY LOW ALTITUDE AND GREAT SPEED). ADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT. PARIS (FRANCE), iEPT NO: AGARD-441, APR 63. ANON, "CHARACTERISTICS OF ATMOSPHERIC TURBULENCE NEAR THE GROUND. VARIATIONS IN SPACE AND TIME FOR STRONG WINDS (NEUTPAT. ATMOSPHERE)," ESDU DATA ITEMS N 75001 JUL 1975, 31 P. ARNOLDI, R.A., "UNSTEADY AIRFOIL RESPONSE," NASA SPEC PURL 207 (BASIC AERODYNAMIC NOISE RESEARCH) JULY 14-15, 1969, P. 247-56. 103

6 1 62ASHBURN, E. V. s, WACO, D, E AND MITCHELF A 7, "OV E`O'ElMENT63 OF HI.1GH, ALT"ITUDE CLEAR AIR TURBULENCE MODEL3,' A R l-03CE ZLiiTT 604 DYNAMICS LABORATORY, WRIG-HT-PATTERSON AFB, OHIlO, AFFDL-T&R0'9-793,33 65 NOV. 1969. 66 67 ASHBURN, ET A.L,"HIGH ALTITUDE CLEAR AIR TURBULENCE MODELS FOR 68 AIRCRAFT DESIGN AND OPERATION,"1 LOCKHEED-CALIFORNIA COMPANY, 69 AFFDL-TR-68-79, JUL 68. 70 7 1 ASHBURN, E.V.,, WACO, D.E., AND MELVIN, C.A., "fDEVELOP~m N T O F 72 HIGH ALTITUDE GUST CRITERIA FOR AIRCRAFT DESIGN." AIR FORCE 73 FLIGHT DYNAMICS LABORATORY, WRIGHT-PATTERSON AFBs OHIO, 74 AFFDL-TR-~7O-101, OCT. 1970. L 7 5 76 ATNIP, F.K. AND GAULT, J., "ANALYSIS OF GUST VELOCITIES FO)R 77 APPLICATION TO AIRCRAFT DESIGN,'# INTERNATIONAL CONFERENCE ON 78 ATMOSPHERIC TURBULENCE, COMP.ILATION OF PAPERS, THE ROYAL 79 AEROINAUTICAL SOCIETY, LONDON, ENGLAND, MAY. 80 81 BAARSPULI M. AND GERLACH, O.H.,r"CALCULATION O,,F THE PESPONSCE 82 OF AN AIRCRAFT TO RANDOM ATMOSPHERIC 'TURBULENCF. PART 2 - (M 83 METRIC NOTIONS," TECHNISCH E HOGESCHOOt. DELFT (NETHERLAND4. DEPT. 84 OF AERONAUTICAL ENGINEERING., REPT HK 1-39, APR 68. 8 5 86 BANNON, J.K., "TURBULENCE IN THE STRATO$_-lPAE9E AND IN THE UPPER 87 TROPOSPHERE," ATMOSPHERIC TURBULENCEH AND ITS RELATION TO AIRCRAFT, 88 ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUG-H, ENGILAND, NOV. 16, 90 91 BARNOSKI, R.L. AND MAURER, J.R., "MEAN-SQUA~RE RESPONSE OF 92 SIMPLE MECHANICAL SYSTEMS TO NONSTATIONAPY RANDOM EXCITATION,"9 93 TRANSACTIONS OF ASME; SERIES E: JOURNAL OF APPLIED MECHANICS, 94 VOL. 36, NO. 2, JUNE 1969, PP. 221-22 7. 95 96 EARROIS, "OA REVIEW OF FRE'NCH W4ORK ON FATIQUE?OR THE IPFRIOD 9 7 1964-1966, AERON. FATIQUE FEB. 1968, 2339-378. 98 99 ~ BATCHELOR, G. K.,"THE THEORY OF HOMOGENOUS TURBULENCE," CAMBFRIIUNIVERSITY PRESS, 195.3, PP. 14-17. BEER., F.P. AND TREVINO, G.,t "ON RESPONSE OF STRUC-TURE V> THROUGH RANDOM FIELD,"l ASME-PAPER 69-VIBP-38 FOR MEETING MAR 30 -APR 2, 1969, 5 P. FABENNETT, FLOYD V. AND PRATT, KERMIT G.,"CALCULATED RESPONSFN, llBST COMPARISONS, NATIONAL AERONAUTICS AND SPACE ADMI41STRTif~ OKLANGLEY STATION, VA. LANGLEY RESEARCH CENTER., REPT NO: NASA-TR~-R-69f 19600. *BERGQUI1ST, RUSSELL R.,"1HEUICOPTER GUST RESPONSE INCLTU))i. VUNSTEADY AERODYNAMIC STALL EftFECTS,"1 Ull"TED AIRCRAFT CORP, ~TP T F') R 1 4 CONNo SIKORSKY AIRCRAFT DIV, FINAL REPT, MAY 73. eRMRAN, S., MAC CREADY, P.B. JR., WEBSTIER, A. A_,D W~_L~lIA;lI 17 R.E., '"OPERATIONAL APPLICATIO11N OF A UNIVERSAL TURBULE NC' MS E A1~15'j SYS'~F,"'EM FINAL REPORT, METEORiOLOGY RESEARCH, ILNC.,f ALTADENA', CALI.; 1 9 REPT N09: NASA-CR-62025, MR.I,6 5-FE&-3O1, NOV 65. JI 04

E I S P) l C; O3 a - IN" > 35RN A D Oi 5RF N ', ' F. u g s T? LCADS ON..iG RPAF ES IH TC GL J O URNAL O " THE. AR'N AJUTCAL. SC^:NCES, wOL. 6, JAN. 1951, P?. 33-42. BiSPLINGHOFF, R. L., ASIHLEY, H., AND HALFMAN, R.L., "DYNA yIC > RESPONSE TO A DISCRETE GUST," AEROELASTICITY, 1ST ED., ADDISONWESLEY, CAMBRIDGE, MASS, 1955, PP. 673-679. ) BLACKMAN, R. B AND TUKEY, J. W, "THE MEASUREMENT OF POWER i SPECTRA," 1ST ED., DOVER, NEW YORK, 1958. BOONE (AIR FORCE FLIGHT DYNAMICS LABORATORY), HIGH ALTITUDE CRITICAL ATMOSPHERIC TURBULENCE DATA SYSTEMS, AFFDL-TR-67-1, ^AY 67 BOUCHER, R. J., "MESOSCALE HISTORY OF A SMALL PATCH OF CLEAR AIR TURBULENCE," JOURNAL OF APPLIED METEORALOGY, VOL. 12, AUG. 1973, PP. 814-821 ** IT IS POSSIBLE THAT RADAR RETURN FROM C.A.T. IN THE *I TROPOPAUSE OR BELOW WILL MASK THE AIRCRAFT VIBRATIONAL ** PROPERTIES IMBEDDED IN THAT C.A.T. THE C.A.T. SEEMS TO ** OCCUR IN REGIONS OF TEMPERATURE INVERSION AND HIGH WIND ** SHEAR (IN THE VERTICAL PLANE). BOUJOT, J., "A LINEAR CONTROL OF SYSTEMS WITH RANDOM INPUT - APPLICATION TO GUST RESPONSE CONTROL," OFFICE NATIONAL D ETJUDES ET DE RECHERCHES AEROS PATIALES, PARIS (FRANCE)., REPT NO.: ONE RA-P-131, 1970. BOWNE & ANDERSON (TRAVELERS RESEARCH CENTER, INC.), "TAKE-OFF AND LANDING CRITICAL ATMOSPHERIC TURBULENCE (TOLCAT) ANALYTICAL INVESTIGATIONS," AFFD L-TR-68-23, APR 68, AD 835 232. EROADBENT, E.G., ZBROZEK, J.K. AND HUNTLEY, E., "A STUDY OF DYNAII( AEROELASTIC EFFECTS ON THE STABILITY CONTROL AND GUST RESPONSE OF A SLENDER DELTA AIRCRAFT," ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH (ENGLAND)., REPT NO: A RC-R/M-3690, ARC-32779, 1972. BRUNING, G., "STATISTISCHE PROBLEME IN DER FLUGMECHANIK (STATISTIC PROBLEMS OF FLIGHT MECHANICS)," DEUTSCHE VERSUCHSANSTALT FUER LUFT-UND RAUMFAHRT E V GBERPFAFFENHOFEN (WEST GERMANY), REPT NO: DVL-305, 1969. BUCCIARELLI, L.L, AND KUO, C., "MEAN-SQUARE RESPONSE OF A SECOND ORDER SYSTEM TO NONSTATIONARY RANDOM EXCITATION," TRANSACTIONS OF ASME; SERIES E: JOURNAL OF APPLIED MECHANICS, VOL. 37, NO. 3, SEPT. 1970, PP. 612-616. BULLEN, N.I., "A REVIEW CF INFORMATION ON THE FPEQUENCE OF GUSTS AT LO W ALTITUDE," AERONAUTICAL RESEARCH COUNCIL, LONDON, C. P. NO. 873, 1966. P ON MICROMETEROLOLOGY, D.A. HAUGEN, ED., AMER. METEOR. SOC., 1-65 BURNHAM, J., "AN EXPERIMENTAL CHECK ON THE THEORETICAL RELATIONSHIP BETWEEN THE SPECTRAL DENSITY AND THE PROBABILITY DISTRIBUTION OF CROSSINGS FOR A STATIONARY RANDOM PROCESS 4ITH GAUSSIAN DISTRIBUTION, USING DATA OBTAINED IN MEASUREMENTS OF AIRCRAFT RESPONSE TO TURBULENT AIR," AERONAUTICAL RESEARCH COUNCIL LONDCN (ENGLAND), REPT. NO: ARC-CP-834, SEPT 1963 BUSCH, N.E., 1973: "ON THE MECHANICS OF ATMOSPHERIC TURBULENCE." 105

WORKSHO -, AND S.E. LARSEN,, 1972- "5L2ECTRA OF, TURBULENCE P'-_ 182THE ATMOSPHERIC SURFAC""E LAYER." RISOG REP. NO. 256, 18 -20 7. '13 41 CAMPAZGNA, A.W. AND PRIi3Y0,r fl."Zo "A STU3Y OF STAk3IL'IZATIOlN TECiiT 1 3 5 FOR SMALL, FIXED-WING, REMOTELY PILOTED AIRCRAFT, "#ARMY ELECTRONICS 186 COMMAND FORT MONMOUTH, N.J., REPT NO.: ECOM-'4239, AUG 7L4 187 188 CANSDALE, RI. AND HALL, H., "GUST RESPONSE MEASUREMENTS ON?A MO ( 18 9 AIRCRAFT,"l ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH (ENGLAND). 19 0 REPT NO.: ARC-CP-11 13, RAE-TR-69273, 1970 19 1 19 2 CARLSON, E. FRANK, "AN INVESTIGATION OF THE POTENTIAL1. Bl.N-EFTTs 19 3 OF DIRECT SIDEFORCE CONTROL FROM A MISSION VIEWPOI.NT," BOEIlN%'; 19 4 AEROSPACE CO SEATTLE WASH RESEARCH AND ENGINEERING DIV, PEPT 195 NO: D180-17508-1, 31 JUL 73. 19 6 197 CASE, E.-R. "A STUDY OF THE EFFECTS OF C L-COUPLING ON THE 198 LATERAL STABILITY OF AIRCRAFT IN ATMOSPHERIC-l TURB3ULENCE" TORNT '199ci UNIV. (ONTARIO). INST. FOR AEROSPACE STUDIES.,. REPT NO.: 200 UTIAS-TN-118, SEP 67 20 1 202 CHALK, CHARLES, "FLIGHT EVALUATICN. OF VARIOUS PH'IGGOID 7iYN P 1IC - 20 3 AND 1/TH 1 FOR THE LANDING-APPROACH TASKol" C3'&N._r~jlL AERO%%AUTIC'.,-AL 2014 LAB., BUFFALO, N~.Y., REFT NO: TCo1K4 DEC 65. 235 205 i CHAN, PAUl. T., O"LOh ALTITUDE PE N-E T i AT IO-N P-ARAMETRIC STUDYr PARC7 207 II, EFFECTS OF ATMOSPHERIC TURBULENC ]~ LOWi ALTITUDE FLIG.HT. PFIRF'OP' 20~ AERONAUTICS DIV. LING-TEMCO-VCUGdT INC. DALLAS, TEXAS, EEPT. NO: LT' 20 9 2-55100/5R-50275t MARCH 1965. 2 10` 2 1 lilCHEN, W.-Y., "APPLICATION OF RICE'S EXCEEDANCE STATISTICS Tn 212 ATMOSPHERIC TURBULENCE," AlAA JOURNAL, VOL. 10s, NO. 8, AUG13. 19 2 13 72, PP. 1103-1105. 214 * SHOWS THAT RICE'S CALCULATION OF EXCEEDENCE STATISTllICS 21 5 DOESN'T REALLY APPLY TO ATMOSPHERIC TURBULENCE BECAUSE 2 1S f) TURBULENCE IS IN FACT STiCNC!2`' eiON GAUSSIAN. 218 CHINTSUN, Hl. AND PI., W.S., "INVESTIGATION O'F!40ORTHRCP >-5A\ Wf1'4 ~19 BUFFET INTENSITY IN TRANSONIC FLIGHT,"1 NORTHROP CORP., HIAWT HNE,, CALUf. AIRCRAFT DIV., REPT NO..: NASA-CR-214814, NOV 714 CHRISTOPHER, R..T AND DUNN, J..H I 'NFLUENCE OF AON-KRJ Z1ONGITT UD I NAL A E ROD `N i MI C CH A RAC T E R!T I CS O N T H E P OW E R S PE C T~AI, RESPONSE OF AIRCRAFT TO1 ATMOSPHERIC TURBULENICE.", AERONAUT Q. V. 214, PART L4, NOV. 1973, P 28'4-294 kZESENTSON, C.C., "f,'N INVESTIGATIONl OF THE POWER SPECTRAL DN1~ OFATMOSPHERIC TURBULEINCE,"1 INSTRUMENTATION LABORATOR"Y - i REllPORT NO.: 644 5-D. 31- MAY 1950. COLEMIAN, THOMAS L. o PRESS, HARRY AND MEADOW.S, MAY T. j"AN rVLVMJ OF EFFECTS OF FLEXIBILITY ON WING STRALINS IN ROUGH AIR -P.P ALARGE SWEPT-WN AIRPLANE BY MEAN~S OF EXPERIMENTALLY DETER<,NE FREQUJENCE -RESPONSE FUNCTIONS WITH AN AISSESSMEN~T OF RANDJOMPROCESS TECHNIQUES EMPLOYEDr NATIONAL AERONAUTICS33 FID t~PACF ADMINISTRATION, LANGLEY STATION, VA. LANGLEY RESEkaC-H NO.: NASA-TR-R;-70, 1960. 239 COLE ~IAN, T.L AN D STLE,~ "ATNOSPHEPZIC TU.RBULENCE ""EX2TJP. 24+C OBTAIMN.D FROM AIRAgLANE A2LA1N ~ tiA ITUDES~ 0 u6

?1,0 0 T FQ ( 7 QO FT FO. R E A A AS O T ALH NO R R 2 EEi.APNER2 II ISA TN D-48 jv960:3 COLSON, D. "METEOROLCGICAL ANALYSIS OF 1964 ICAO TU:.33JLENCE DATAh, WEATHER FUREAU TECHNICAL MEMO, ENVIRONMENTAL SPACE AND SCIENCE ADMINISTRATION, TDL 14, OCT. 1968. CONNER (LOCKHEED-CALIFORNIA COMPANY) PRELIMINARY DESIGN STUDY FOR A HI-HICAT VEHICLE AND INSTRUMENTATION SYSTEM, AFFDL-TR-66-100, ) OCT 66, AD 809 829 COUPRY, G., "CRITICAL ANALYSIS OF THE METHODS USED FOR PREDICTING THE RESONSE OF LARGE FLEXIBLE AIRCRAFT TO CONTINUOUS ATMOSPHERIC TURBULENCE," AIAA PAPER NO. 71-342, APRIL 1971 ** IT IS CLAIMED THAT SPANWISE VARIATIONS IN TURBULENCE ** LENGTH CAUSE ENOUGH CANCELLATION OF LIFT AS TO SMOOTH ** OUT THE PREDICTED RIDE. FOR THE PURPOSES OF RADAR ** MODULATION BY ELASTIC MODES, THIS IS IMPORTANT BECAUSE ** IT MEANS THAT SIMPLER THEORIES ("CYLINDRICAL" WAVES) W * WILL OVERPREDICT THE AIRCRAFT RESPONSE. NEVERTHELESS, ** THERE IS A SCALE FACTOR INVOLVED, I.E. THE LENGTH OF ** COHERENCE OVER THE WINGSPAN AND FOR FIGHTER ** AIRCRAFT THIS SCALE MAY BE LARGE ENOUGH TO ALLOW A ** CYLINDRICAL WAVE ASSUMPTION. EVEN FOR AN AIRCRAFT AS ** LARGE AS THE CONCORD, THE SPANWISE EFFECTS ONLY REDUCE ** PEAK RESPONSE BY A FACTOR OF TWO. FOR FIGHTER AIRCRAFT ** THE ERROR DUE TO THE CYLINDRICAL ASSUMPTION MUST BE ** ABOUT 10%. COUPRY, GABRIEL, "PROBLEMES DU VOL EN TURBULENCE." (PROBLEMS OF FLIGHT IN TURBULENCE," INT COUNC OF THE AERONAUT SCI (ICAS), 9TH CONGR. PROC. HAIF A, ISR, AUG 25-30 1974 V 2: STRUCT. MATER, DYN, PROPUL. DES, NOISE AND POLLUT P 561-574. COUPRY, G., RAPID EVALUATION OF THE STATISTICAL CHARACTERISTICS OF AN AIRCRAFT IN ATMOSPHERIC TURBULENCE, FRANCE. OFFICE NATIONA.L D ETUDES ET DE RECHERCHES AEROSPATIALES, CHATILLON-SOUS-BAGNEUS., REPT NO.: TP-256/1965/, 1965. COX, R.A., "COMPARATIVE STUDY OF AIRCRAFT GUST ANALYSIS PPOCEDURES$ A ERON J V. 74, N. 718, OCT. 1970, P 807-13 CROOKS, ET AL (LOCKHEED- CALIFORNIA COMPANY), HIGH ALTITUDE CLEAR AIR TURBULENCE, AFFDL-TR-65-144, SEP 65, AD 474 616 CROOKS, W.M., HOBLIT, P.M., AND PROPHET, D.T., "PROJECT HICAT. AN INVESTIGATION OF HIGH ALTITUDE CLEAR AIR TURBULENCE," AI. FCECE FLIGHT EYNAMICS LABORATORY, WRIGHT-PATTERSON AF3, OHIO, AFFDL-TR-67-123, NOV. 1967. CROOKS, W.M., HOBLIT, F.M., AND MITCHELL, F.A., "PROJECT HICAT. HIGH ALTITUDE CLEAR AIR TURBULENCE MEASUREMENTS AND METEOROLOGICAL CORRELATIONS," AIR FORCE FLIGHT DYNAMICS LABORATORY, WRIGHTPATTERSON AFB, OHIO, AFFDL-TR -68-127, NOV. 1968. CROSS, A.K., T-38 DYNAMIC RESPONSE GUST LOADS COMPARISON BFTWEEN FLIGHT TEST AND ANALYTICAL RESULTS, NCRAIR DIV NORTHROP CORP, HAWTHORNE, CALIF., REPT NO.: NOR-60-306, IAR 64 DIEDERICH, F.W., "THE RESPONSE OF AN AIRPLANE TO RANDOM ATMOSPHERIC 107

301 DISTURBANCES," REPT NO. 1345, 1958, NACA: SUPERSEDES TN 3910, N\CA. 302 303 DIEDERICH, F.W., "THE DYNAMIC RESPONSE OF A LARGE AIRPLANE 304 TO CONTINUOUS RANDOM ATMOSPHERE, J.A.S., VOL. 23, OCT. 1956. 305 306 DONALDSON, C. DUP. AND SULLIVAN, R.D., "THE APPLICATION OF 307 INVARIANT MODELING TO THE CALCULATION OF ATMOSPHERIC TURBULENCE," 308 AFFDL TR-71-168, JAN. 1972, AIR FORCE FLIGHT DYNAMICS LAB., 309 WRIGHT-PATTERSON AIR FORCE BASE, OHIO. 310 311 DONELY, P., "ATMOSPHERIC TURBULENCE AND THE AIR TRANSPORTATION 312 SYSTEM, "PROCEEDINGS, INTERNATIONAL CCNFERENCE ON ATMOSPHERIC 313 TURBULENCE, LONDON, ENGLAND, ROYAL AERONAUTICAL SOCIETY, 1971, 314 PP.14. DRYDEN, H.L., "A REVIEW OF THE STATISTICAL THEORY 315 OF TURBULENCE," TURBULENCE, EDITED BY S.K. FRIEDLANDER AND L. 316 TOPPER, INTERSCIENCE, NEW YORK, 1961, PP. 115-150. 317 318 DUTTON, J.A., THOMPSON, G.J., AND DEAVEN, D.G., "THE PROBADILI. 319 STRUCTURE OF CLEAR AIR TUEBULENCE-SOME OBSERVATIONAL RESULTS 320 AND IMPLICATIONS," CLEAR AIR TURBULENCE AND ITS DETECTION, 321 EDITED BY Y. PAO AND A. GOLDBERG, 1ST ED., PLENUM, NEW YORK, 322 1969, PP. 183-206. 323 324 DUTTON, J.A., AND H.A. PANOFSKY^i, 970: CLEAR AIR TURBULENCE; 325 A MYSTERY MAY BE UNFOLDING. SCIENCE, 167, 937-944. 326 327 DUTTON, J.A., AND DEAVEN, D.G. 1969: "A SELF-SIMILAR VIEW OF 328 ATMOSPHERIC TURBULENCE." RADIO SCI., 4, 1341-1349. 329 330 DUTTON, JOHN A. PROBABILISTIC DETERMINATION OF AIRCRAFT RESPON 331 TO TURBULENCE AT LOW ALTITUDES, AERONAUTICAL SYSTEMS DIV 332 WRIGHT-PATTERSON AFB, OHIC, DEPUTY FOR ENGINEERING, TECHNICAL 333 REPT. MAY 68-NOV 67, OCT. 68 334 335 EGGLESTON, JOHN M. AND PHILLIPS, WILLIAM H., "THE LATERAL BRES 336 OF AIRPLANES TO RANDOM ATMOSPHERIC TURBULENCE,' NATIONAL AER)NA[T7TC 337 AND SPACE ADMINISTRATION, LANGLEY STATION, VA., LANGLEY 338 RESEARCH CENTER., REPT NO.: NASA-TR-R-74, 1960. 339 340 EMERNBERGER, L.J., "METEOROLOGiCAL ASPECTS OF HIGH ALTITUDE 341 TURBULENCE ENCOUNTERED BY THE XB-70 AIRPLANE," PROCEEDINGS, THI 9) 342 NATIONAL CONFERENCE AERCSPACE METEOROLOGY, NEW ORLEANS, AMERICAAi 343 METECROLOGICAL SOCIETY, 1968. PP. 515-522..4 4 345 EHERNBERGER, L.J., "ATMOSPHERIC CONDITIONS ASSOCIATED WITE 346 TURBULENCE ENCOUNTERED BY THE XB-70 AIRPLANE ABOVE 40,000 VFEET 34' ALTITUDE," TN D-4768, 1968, NASA. >EH EHERNBERGER, L.J., AND LCVE, B.J., HIGH ALTITUDE GUST.ir CELERT IO ENVIRONMENT AS EXPERIENCED BY A SUPERSONIC AIRPLANE, NATIONA i 35% AERCNAUTICS AND SPACE ADMINISTRATION. FLIGHT RESEARCH CENTER, 2 t EDWARDS, CALIF., REPT NO: NASA-TN-D-7868, H-836, JAN 75. 353 354 EHLERS, H.L., "TECHNICAL CONSIDERATIONS IN THtE DESIGN OF G{ST 355 ALLEVIATION CONTROL SYSTEMS," AUTONETICS REPORT X7-9)3/301, AN01 iS 356 CA, APRIL 1967. 35 7 358 EICHENBAUM, F.D., "THE APPLICATION OF MATRIX METHODS TO CL.EAR 359 AIR TURBULENCE MEASUREMENT," AIAA PAPER 66-967, BOSTON, MAS:., 360 1966. 108

-I 2 ICHEA ' j M^t FD. D A GI GZ OE'iAL TLHEORY OE AIRCR AFT RESPONSE TC i$tE 'E-DIMEAS#ISNAL TU RBULECE,' JOURNAL O. A:RCRAFT, VOL 8, 4 NC. 5, MAY 1971, PP.353-360. * A DETAILED ThEORY TO PREDICT SYMMETRIC AND ANTI-SYMMETRIC ** RESPONSE TO 3-D TURBULENCE. USES ASSUMPTIONS OF HOMO7 ** GENEITY, STATIONARITY, ISCTROPY AND TAYLOR'S HYPOTHESIS. 9 EICHENBAUM, FREDERICK D., EVALUATION OF 3-D TURBULENCE TECHO NIQUES FOR DESIGNING AIRCRAFT, LOCKHEED-GEORGIA CC MARIETTA*AIR FORCE FLIGHT DYNAMICS LAB. WRIGHT-PATTERSON AFB, OHIO, FINAL 2 REPT. 1 OCT 73-15 APR 75, JAN 75. 3 et EICHENBAUM, FREDERICK D., RESPONSE OF AIRCRAFT TO THREE DI5 MENSIONAL RANDOM TURBULENCE, LOCKHEED-GEORGIA CO MARIETTA, TECHNICAL 6 REPT. JUL 71-MAR 72, OCT 72. EICHENBAUM, F.D., "NEW METHOD FOR COMPUTING THE DYNAMIC RE3 SPONSE OF AIRCRAFT TO THREE-DIMENSIONAL TURBULENCE," AIAA/ASME 10 S STRUCTURES, STRUCTURAL DYNAMICS & MATLS CONFERENCE — TECH PAPERS FOR MEETING, NEW ORLEANS, LA, APR 14-16, 1969, P. 84-94. ELDERKIN, ET AL. (BATTELLE MEMORIAL INSTITUTE, PACIFIC NORTH WEST LABORATORY), TAKE-OFF AND LANDING CRITICAL ATMOSPHERIC TURBULENCE (TOLCAT) - EXPE RIMENTAL INVESTIGATION, AFFDL-TP-70-117, MAY 71, AD 885 321.? ELDERKIN, ET AL. (BATTELLE MEMORIAL INSTUTUDE - PACIFIC NORT HWEST LABOR ATORY), TAKE-OFF AND LANDING CRITICAL ATMOSPHERIC TfU BULENCE (TOLCAT) - EXPERIMENTS AND ANALYSIS, AFFDL-TE-71-172, APR 72, AD 750 131. ENDLICH, R M. AND MCLEAN, G.S., "EMPIRICAL RELATIONSHIPS BETWEEN GUST INTENSITY IN CLEAR-AIR TURBULENCE AND CERTAIN METEOROLOGICAL QUANTITIES," JOURNAL OF APPLIED METEOROLOGY, VOL.4, APRIL 1965, PP. 222-227. ** AN ATTEMPT TO PREDICT MODERATE OR SEVERE TURBULENCE FROM ** MEASURABLE ATMOSPHERIC QUANTITIES, E.G. THE PRODUCT OF ** WIND SPEED AND TURNING OF THE WIND WITH HEIGHT, OR VERTICAL ** SHEAR OR RICHARDSON'S NUMBER. A FREQUENCY OF OCCURENCE ** GREATER THAN 50X CAN BE PREDICTED WITH THESE OBSERVABLES ** (NONE OF THE MEASURED QUANITIES CAN BE MEASURED BY RADAR, ** HOWEVER). ENDLICH, B.M. AND MANCUSO, R.L., "THE TURBULENCE CLIMATOLOGY OF THE UNITED STATES BETWEEN 20,000 AND 45,000 FT. ESTIMATED FRCO AIRCRAFT REPORTS AND METEOROLOGICAL DATA," CONTRACT AF19 (628)-5173, JUNE 1968. STANFORD RESEARCH INSTITUTE, MENLO PARK, CA. EPPS, J.B., LIBERTY, S.R., FERRY, D.K. AND SEECAT, R.H.. "OUTPUT ACAPTIVE DYNAMIC MODEL FOR ESTIMATING TURBULENCE." MIDWEST SYMP ON CIRCUIT THEORY, 16TH, PROC, PAP, UNIV OF WATERLOO, ONT, APR 12-13, 1973 V.1, PAP VII. 4, 10 P. ETKIN, B., JOHNSTCN, G.W. AND TEUNISSEN, H.W. "MEASUREMENTS OF TURBULENCE INPUTS FOR V/STOL APPROACH PATHS IN A SIMULATED PLANETARY EOUNEARY LAYER." TORONTO UNIV INST AEROSP STUD UTIAS REPT NO 189, JUL 1973, 90 P. ETKIN, B., "THEORY OF THE FLIGHT CF OF AIRPLANES IN ISCTROPIC 109

4i21 TURBULENCE - REVIEW kbiD ET~lSI0N," AEV-ISORY GROUi? ZOR AERONAUTICAL 2.2 RESEARCH AND DEVELOPMENTs 2ARIS, (FRANCEW),, -RhT.NO AGARD-2372,, A73?R. 4213 424 FICUTER, D., CALCULATION OF THlE FREQUENCY RESPONSE OF THE 42 5 ELASTIC AIRPLANE'S REACTIONS TO VERTICAL GUSTj.S AT INCOMPREZSSTELE 42 6 FLOW, DEUTSCHE VERSUC HSANSTALT FUR LUFT- UIND RAUIFAHR-L. OVER427 PFAFFENHOFEN (WEST GERMANY). INSTITUT FUER FUGMECHANIK.,, REEPT NO: 42 8 DVL-821, DLRFB-69-040 JAN 69 429 4 30 FIREBAUGH, J.M., "EVALUATIONS OF A SPECTRAL GUST M~CDEL UJSlNG 43 1 VGH AND V-G FLIGHT DATA,"1 J. AIRCRAFT, 4:6, 518-525s, NOV-DEC 1967. 432 * AN EXCELLENT OVERVIEW OF THE RESPONSE TO TURBULENCE 433 * PROBLEM. GIVES GUST INTENSITY PARAMETERS, FLIGHT TIMl`;. 434 * IN TURBULENCE AS FUNCTIONS OF ALTITUDE. MUCH EXPERIMENTAL 4 3 5 DATA ARE GIVEN, BUT FOR A RATHER OID FLEET OF C-130, 43 6 L* -749, L-188 AND B-720B AIRCRAFT. 437 4 38 FRANKLIN, J.A., "TURBULENCE AND LONGITUDINAL FLYING QUALITIESI` 439 NASA CONTRACT REPT CR-1821, JULY 1971. 440 44 1 FRICK, J.K. AND JOHNSON, W., OPTIMAL CONTROL THEORY 1TNV1EST1 -442 GATION OF PROP ROTOR/WING RESPONSE TO VERTICAL GUST, NA-1IO0NAL 44 3 AERONAUTICS AND SPACE ADMINISTRATION. AMES RL>E3)ARCH CENTEF,<)FT 444 FIELr, CALIF., REPT NO: NASk-TM-X-6 L2'k, SEPT 74. 445 446 FUJIMORT, Y. AND LIN, Y.K., "ANALYSI11S OF AIRPLANE FESPONSE 44 7 TO NONSTATIONARY ATMOSPHERIC 'TURBULENCE INCLUDING WING BENDING 44 8 FLEXIBILITY," AIAA JOURNAL, VOL. 11, NO. 3j, ~1ARCH 1973, PP. -3314 44 9 -339. 4 50 451 FUJIMORI, YOSHINORIa, AND LIN., Y.K.j, "ANA laY IS OF AIRPLANE 452 RESPONSE. TO NONSTATIONERY TURBULENCE INCLUDING WING"` BENDING FEI 453 BILITY. PART Ile" AIAA JOURNAL, V. 11, NO. 9,j SEPT 1973, PP. 1343 -454 * IHIS PAPER IS NEEDED TO SAKE THE PREVIOUS ONE BY FUJIMORI 455 * AND LIN IMPORTANT. HERE IT IS SHOWN THAT SUDDEN ONSET OF 45 6 STATIONARY RANDOM FORCING CAN' Cs-AUSE 28% YIORE ACCELERATION 457 * AT THE AIRCRAFT C.G. THAN STATOA1:1RY RAN3OM FOR"'-ING. 45 8 PERHAPS THIS CORRECTION FACTOR SHOULD BE APL2LIED IN 459 * DESIGN- SOMETHING LIKE A SHARP-EDGED GUST. FUJJIMORI, YOSHINORI, "'ShEAR AND MOMENT RESPCINSE, OF ath'-~ A~~ PLN5WN-T ONTTONARi TURBULENCE." AIAA JOURNAL VOL. ~,4 NO. 11, NOV 1974, PP. 1459-1460. FUJIMOBIj, Y.,r SHEAB AND MOMENT RES-PONSE OF THE AIR6 ~?LALNE WING TO NONSTRTICNARY TURBULEINCEj, NATIONAL AEROSPACE, -LAL.w TOKYO (JAPAN) v REPT NC: NAL-TR -40 4T, JAN 75. FULLER, J.R.,o RICHMONDa, L.D. ET AL., "CONTRIEN1MTIONS T ki' DEVELOPMENT OF A POWER-SPECTRAL GUST DESIGN PROCEDUBE FOih &v IA AJ CRAFT," BOEING RENTON, FAA-ADS-54v JAN. 1966. FULLER, J.R.j, ##A PROCEDU~RE FOR EVkLUA.LI4G Ah C~S ~ T i TTION S OF CO0NT I NUOU S 'TU R BU LEN CE ON A I PP LA NE L~R SON SET3, J IF OF AIRCRAFT, VOL. 5,v NO. 1, JAN-FEB 1968, PP. 49b **'7 A FAIRLY EASIC APPROACH AT PROVIDING IN LH INTO D **EFFECTS IN RESPONSE TO TURBULENCE. 44 9 FU NG s Y. C., A N I N TRODU CTIO N TO T HE T HEO0R Y O,)F A ERGE L AS7UJ" VT,,I~ 4 8 01 WILEY, NEW YORK$ 1955. I110

FUNA, Y13C2 S.ATISTICAL ASPECT CF DYNA~MIC LOAD," JOURNAL CF AR SG ATICL SCIENCES, VOL. 20d MAY 1953,?P. 31 7-330 PUNGI Y.C., AN INTRODUCTION TO THE THEORY OF ELASTICITY. DOCVER, NEW YORK, 1969, PP. 280-281. GAULT, LOW ALTITUDE ATMOSPHERIC TURBULENCE LO-LOCAT MID-TERM TECHNICAL DATA ANALYSIS, (THE BOEING COMPANY), SEG-TR-67-35, AUG 67, AD 820 880. GAULT, J.D. AND GUNTER, D.E., JR., "ATMOSPHERIC TURBULENCE CONSIDERATIONS FOR FUTURE AIRCRAFT DESIGNED TO OPERATE AT LOW ALTITUDES," JOURNAL OF AIRCRAFT, VOL. 5, NO. 6, NOV.-DEC. 1968, PP. 574-577. * VERIFIES THE VON KARMAN MODEL OF THE POWER SPECTRUM FOR ** ATMOSPHERIC TURBULENCE GIVES SOME ADVICE ON LENGTH SCALES ** OF TURBULENCE FOR SEVERAL MODELS. GAULT, J.D., "LOW ALTITUDE ATMOSPHERIC TURBULENCE ANALYSIS METHODS, " CANADIAN AERONAUTICS AND SPACE JOURNAL, VOL. 13, NO. 7, SEPT. 1967, PP. 307-314. GAULT, ADDITIONAL RESEARCH OF LOW ALTITUDE TURBULENCE DATA, (THE BOEING COMPANY), AFFDL-TR-71-150, SEP 71, AD 739 875. GENERAL DYNAMICS, SAN DIEGO, CALIF. CONVAIR AEROSPACE DIV, "CONTROL POWER CRITERIA FOR STATICALLY UNSTABLE AIRCRAFT," REPT NO: CASD-NSC-76-003, NOV 76. GERLACH,O.H., VAN DE MOESDIJK, G.A.C. AND VAN DER VAART, J.C., "PROGRESS IN THE MATHMATICAL MODELLlNG OF FLIGHT IN TURBULENCE," FLIGHT IN TURBULENCE, AGARD CP-140, 1973, PP 5.1-5.38 GIESING, J.P., STAHL, B., AND RODDEN, W. P., "ON THE SEARS FUNCTICN AND LIFTING SURFACE THEORY FOR HARMONIC GUST FIELDS,"DOUIGLAS PAPER 5368, MARCH 1969, DOUGLAS AIRCRAFT CO; ALSO JOURNAL OF AIRCRAFT, VOL., NO.3, MAY-JUNE 1970, PP. 252-255. ** THIS WORK APPEARS TC HAVE BEEN MOTIVATED BY THE EXPENSE ** OF THE DOUBLET LATTICE METHOD FOR CALCULATING UNSTEADY LOADS ** DOE TO HARMONIC GUSTS. BECAUSE A GUST OF ARBITRARY PROFILE 4* REQUIRES A WIDE HARMONIC CONTENT TO DESCRIBE IT, MANY ** rISCRETE FREQUENCY CALCULATIONS WERE PREVIOUSLY REQUIRED, ** PARTICULARLY BECAUSE THE SEARS FUNCTION IS SO RAPIDLY VARYING. ** BY TRANSFORMING THE ORIGIN (WHERE THE GUST VELOCITY HAS ** "ZERO PHASE ANGLE") TO THE LEADING EDGE, THE SEARS FUNCTION ** S SUITABLY TAMED SO THAT INTERPOLATION IS POSSIBLE. GOBELTZ, J., LABORATORY FLIGHT SIMULATION WITH FREE-FLI';HT MODELS, KANNEkR (LEO) ASSOCIATES, REDWOOD CITY, CALIF., REPT NO: NASA-TT-F-17124, AUG 76. GOGOSHA, OREST R. AND MORIARTY, THOMAS E., THE RESPONSE OF A HOVERING V/STOL AIRCRAFT TO DISCRETE IURBULENCE, REPT NO: SGC/EE/ 67-7, JUN 67. GOSSARD, E.E., J.H. RICHTER AND D. ATLAS, 1970: INTERNAL WAVES IN THE ATMOSPHERE FROM HIGH RESOLUTION RADAR MEASUREMENTS. JOURNAL GEOPHYS. RES., 75, 3 523-3536. 111

54 GVIFEIN, C. JR AIND LAAj-GNEj, A. H4., THEE2R LTO OF THF. SCAT ~42 TERING CROSS-SECTIONS 0F THE DISTURBED T.NDEX QF REFFACT720N A.ND -0 THE ACCELETRATION INCREME~NT OF A CONVENTIONAL" AllZCRAFT DUE T C 544 CLEAR AIR TURBULENCE, TEXAS UNIV AUSTIN ANTENNAS AND PROPAG.AT; ON1011 -54 5 LARTNO P-28t 28 MAY 68. 546 547 GUNTER, ET 4L., LOW ALTITUDE ATMOSPHERIC TURBULENCE LO-L1OCAT 548 PHASES I AND II, THlE BOEING COMPANY, ASD-TR-69-12, FEI3 69,, AD 549 853 299. 550 551 HALL ER, P~.L. A ND P EL OUDBET, R. P. J R PAkR A MET RIC S TU DY O F B3- C 552 ACCELERATION RESPONSE TO IURBULENCE AND CCMPARISONS WITHi FLI(;IiT 553 DATA, AUGUST 1967 - AUGUST 1968, GENERAL DYNAMICS-FORT WORTH,71 554 TEX.,v REPT NO.: NASA-CR-66699,, NOV 68. 556 HAMEL, P., ON THE EFkECT OF GUSTS AND CROSSWIND ON THE DY557 NAMIC RESPONSE OF AIRCRAFT. ESTABLISHMENT, FARNBOROUGH (PN~3LAND)) 558 REPT NO: RAE-LIB-TRANS-15-24, OCT 70. 559 56U HAMEL, P. GUST EFFECTS ON THE DYNAMICS OF kIRCRAFi DURING 55 6 1 LANDING APPROACH, NATIONAL AERONAUTICS AND SPACEAYIiATFN 562 WASHINGTON, D.C.,f REPT NO.: NASA-TT-F-12751, MAY 71 563 564 HAMMOND, J.K., " ON THE EP ~&E AND MULjTIDEGRfp, OF 565 FREEDOM SYSTEMS TO NON-STAT&l- 1.~Ai~fl IM7) X t.TA.OS ORN 566 0F SOUND AND VIBRATION, VOL. 7, 196a, 3 393- 4 16. 567 56`8 HARDY, K.R. AND OTTERSTEN K* "RADAR INVESiTI,(2AT.1IONS 0?7 CYI56 9 VECTIVE PATTERNS IN THE CLEAR ATMOSPHERE," JOURNAL OF ATMOSUFNP.tC 570 SCIENCES, VOL. 26, JULY 1969, PP. 666-672. 571 * TWO TYP ES OF CLEAR AIR CONVECTIVE PATTERNS A&R OBSERVED AITH 572 * RADARs, A SMALL DOUGHNUT TYPE AND A BERNARD TYPE. T HlE FFIR ST 573 * TYPE IS 1~-3 KM IN DIAMETER AND SEVERAL HTINDRE"D M~ETERS IN HIEIHT 57 4 AND PERSISTS FOR 20-30 AINUTES. THE SECOND TYPE IS 5-""0 KM 5 7 **l IN DIAMETER AND 1 -2 KM IN HEIGHT. 576 577 EIARRINGTON, CHARLES A. IIA-1, DE.L" OF C"lf-,)NTBOL SYSTEM TO 578 SThB~LILIZE THE AFT FUSELAGE OF A B- 52 BOMBER 'LeI THE PRESENC"T, O)F 5 7 '9 A RANDOM WIND GUST, AIR FORCE INST OF TECH, WR`AGPIT-?ATT~lfSO)N, AF93, ~8OOHIO SCHOOL OF ENGINEERING,. liEPT NO: G"E/'ZE/7L4Ml-5,r MAR 74. 32HILDRETH, ET AL. HIGH AILJITUDE CLEAR A~IR TURBUlLvENCE, L0CTh T) CALIFORNIA COMPANY, ASD-TDR-63-4440, SE? 6-3, AD ~421 857. HINZEv J.0.,v TURBULENCE., AN INTRCDUCTION TO ITS MECHAN IS1 AUU) THEORY, MC GRAW-HILLt NEW YORK, 1939,r P. 147. fiOBLIT* F.$4., PAULs, N.,p ET AL.,q "DEVELOPMENT OF POIE?-, F&-, TRAL GUST DESIGN PROCEDURL FOR CIVIL AIRCRAFT," LOCKHEED CA L F. ~,j FAA-ArS-53a, JAN. 1966. HOUBOLT, J. C., "ATMOSPHERIC CATURBULENCE",, DtEYDEN aESEtjRflCr! LECTURE, AlAA OCURNALs, VOL. 11, NO. 4, APRIL8j 1973.1,P. 2I4 GOOD SUMMARY OF TURBULENCE.A- II J Y,!1. Z INCLUDEFS flTKL DF7PI'T LO 9"FOR ORIGIN OF TURBULENCE, VON KAVMAN,'S - AIEsT ~), C 2WT 5 9 SPECTRA FOR ISOTJROPIC TURBULENCEv AND zRATI "5OF q 7 *CCCURRENCE OF VARTOtJS SIZ1Z25 AND) VELOCITY TNTFNUTTTFJ"_ OF TURBULENCE PATCHES.- EIlPHASIZES FANOOM INP~UT F OR 01EaS.IG N. 591 * * AND SFIG WS 'T.; EQ UIV AL.EXCE BET', —, E"N?A.ND OM 2X'-"`CT 1 AMIO','N D E S TCN, It 0 01** LAWS AND GU.;i) DESIO2 LATE. __T IM'f>S:'t-CRA"T `

1r TiJR3Pi: T PCnS '7 O'?H TII-,; " 1,.00, O40,000 FT:i`NGE. 2 3H0 OLT^ u DESIG HA;UAL 1"OR V E'TICTAL GUSTS BASED ON POYEE SECTRAi T CHNIQUi ES APFDL-T- '70 106, T EC. 1970, AIR FCRCE FLIGHT DYNAMICS LAB., WRIGhT-PATTERSON AIR FORCE EASE, OHIO. 7 HOUBOLT, J.C., "THE ART Of DETERMINING GUST FREQUENCE RESPONSE FUNCTIONS," PRESENTED AT THE 31ST AGARD STRUCTURES AND MATERrALS PANEL MEETING, TONSBERG, NORBAY, OCT-NOV 1970. ) 1 HOUBOLT, J.C., "MATHEMATICAL MODELING AND RESPONSE EVALU'ATION FOR THE FLUCTUATING PRESSURES OF AIRCRAFT BUFFETING," ADVISOrY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT, REPT. NO: AGARDR-630o JULY 1975 HOUBOLT, J.C. "GUST DESIGN PROCEDURES BASED ON POWER SPECTRAL TECHNIQUES," AFFDL-TR-67-74, AUG. 1967, AIR FORCE FLIGHT DYNAMICS LAB., IRIGHT-PATTERSON AIR FORCE BASE, OHIO. S?OUBOLTo J.C. "ON RESPONSE OF AIRPLANES IN A 3-DIMENSIONAL GUST FIELD, " REPT 161, JULY 1971. AERONAUTICAL RESEARCH ASSOCIATES OF PEiNCETON INC., PRINCETON, N.J. HOUBOLT, J.C., "AIRCRAFT RESPONSE TO TURBULENCE INCLUDING WAKES," AIRCRAFT WAKE TURULENCE AND ITS DETECTION. PLENUM PRESS, NEW YORK, 1971. HOUBOLT, J. C., "ON THE RESPONSE OF STRUCTURES HAVING TULTIPLE RANDOM INPUTS," WGL JAHRBUCH (FREDERICK VIEWEG UND SOHN, BRAUNSCHWEIG, GERMANY, 1957), PP. 296-305; ALSO PAPER DK 533.6.013.08, 517.512 (1957). HOUBOLT, J.C. AND SEN, A., "CROSS-SPECTRAL FUNCTIONS BASED ON VON KARMAN'S SPECTRAL EQUATION," CR-2011, MARCH 1972, NASA. HOUBOLT, J.C., STEINER, R., AND PRATT, K.G., "DYNAMIC RESPONSE OF AIRPLANES TO ATMOSPHERIC TURBULENCE INCLUDING FLIGHT DATA ON INPUT AND RESPONSE," TR R-199, 1964, NASA. HOUBOLT, JOHN C., "PIELIMINARY DEVELOPMENT OF GUST DESIGN PROCEDURES BASED ON POWER SPECTRAL TECHNIQUES." VOLUME I. THEORETICAL AND GENERAL CONSIDERATICNS, AERONAUTICAL RESEARCH ASSOCIATES Of PBINCETON, INC., N.J., REPT NO.: ARAP-83-VOL-1, JUL 66, AND VCLUME II. SUMMARY OF POSSIBLE PROCEDURES, REPT. NO: ARAP-83-VOL-2, MARCh 1966. HOUBOLT, JOHN C., "EFFECT OF NONUNIFORM SPANWISE GUSTS -(" AIRCRAFT VERTICAL RESPONSE," AERONAUTICAL RESEARCH ASSOCIATES '? PRINCETON, INC, N.J., REPT NC: ARAP-209, JAN 74. HOUBOLT, JOHN C.o "ON THE RESPONSE OF AIRPLANES IN A THREEDIMENSIONAL GUST FIELD," AERONAUTICAL RESEARCH ASSOCIATES OF PRINCETON, INC., N.J., REPT NC: ARAP-161, NOV 72. HOUBOLT, JOHN C. AND WILLIAMSON, GUY G,, "SPECTRAL GUST RESPONSE FOR AN AIRPLANE WITH VERTICAL MOTION AND PITCH," AERONAUTICAL RESEARCH ASSOCIATES OF PRINCETON INC NJ, REPT NO: ARAP-256, NOV 75. HOUBOLT, JOHN C. AND WILLIAMSON, GUY, "A DIRECT TIME HISTORh' STUDY 113

C61 OF THE RESPONSE OF AN AIRPLANE TO NONSTA7'IO'NF~R`N URBUJLENCE04 662 AERONAUTICAL fRESEj'.jARCHi ASSOCIATES OF PRXNIC.ETLON ILNC N.J. *AT11 7?C-C2 6 31 FLIGHT DYNAMICS LAB., WRIGL!T-PAT TERSON AFE3 iL. R-LP~7 N'o: b64 ARAP-230, JAN 75. -66 5 666. HOWELL, L.J.o AND LIN, Y~.K., "RESPONSE OF FLIGHT VEHICLES 7') 667. NONSTATIONARY ATMOSPHERIC TURBULENCE," AIAA JOURNAL, VOL. 9, 66 8. NO0. 11, NOV. 1971, PP. 2201-2207. 66 9 A STUDY OF PLUNGING MOTION DUE TO ONSETA OF A PATCH OF TUDflLENC6 70 U ITH EXPONENTIALLY GROWING PROF-ILE OF [EXP(-AT)-EXP(-BT) 1 671 * CHARACTER. CAN BE MADE TO GIVE A RAPID OR SLOW ONSrlET O F A 672 * STATIONARY RANDOM LOADING. 67 3 6 74 HOWELL, L.J., "RESPONSE OF FLIGHT VEHICLES TO NO'NSTATION r R Y 675 RANDOM ATMOSPHERIC TURBULENCE," PHd.D. DISSERTATION, FEB. 19471, 676 UNIVERSITY OF ILLINOIS, URBANA, 1LL. 677 678 HUNSAKER, J.C. AND WILSON, E. B., "REPORT ON BEHAVIOR OF AERO-~ 679 PLA NE S I N G UST S" R EPT. 1, 19 15, NAC A. 680 681 HUNTER, PA. A, "TURBULENCE EXPERIENCE IN A R -QKVNE OVE RA T ION$, 682 MEETING ON AIRCRAFT RESPONSE TIO TURBULENCE, LAM(,LFY, IVA., r NSAf 683 1968, PP. 20.1-20.1 M. 684 685 HUSTON, W. B. AND SKOPINS~I, H~., " Ot3P~iLl'iY AND FIREQ~l ENCY 686 CHARACTERISTICS OF SOME FLIGSHT BUFFET LTiS* 73,15, AA 687 688 HWANG, CHINTSUN, KAMBERG, B.D. AND Pl, W.S. AND CROSS, A. K~., 689 CALCULATICNS ON PROVEN TRAINER AND FIGHTER AIRCRAFT FOR THE 690 VERIFICATION OF A GUST CESIGN PROCEDURE,"1 NORAi17.R DIV NORTHRCP CCiU? 691 HAWTHORNE CALIF, REPT NO.: NOR- 66-149, JUL 66. 692 693 HWANG, C. AND PI, W.S., "T{NOI UFE FHVOFO N RTMP, 694 F-5A AIRCRAFTs" ADVISORY GROUP FOR~ AEROSPACE RESEARCH AND DEVELOLP2 695 PARIS (FRANCE), REPTL. NC: AGIAE~D-R-624, SEPT. 1974 696 B* UFFETING IS A RELATIVELY ~iiGl3 I?REQTJENCY PHECNOMENON, AT 50-200 697 * IT DOES EXCITE RIGID BODY TRAN3L.4&'lI0"N AT THIFSE FEQUENCS.'lEj3. 698 919 ~II, J.M, AND SIDWELL, K.W.o "EVALUA~LCION OF UNSTEkafJY AE-'-3YNMl~l1( 700 FORC`_ES AND DYNAMIC RESPONSE OF FLEXIBIE AIRCRAFT STRUJCTURE C CONTINUOUS TURBULENCE I I2~OI LGT"PO~D!SO A 0 ~8TH STRUCTURES, STRUCTURAL DYNAMICS AND MATERIALS CONFE[XENCL", VSPRINGSo CA, MARCH 29-31 19607, PP 380-390. **THE AUTHORS POINT OUT 'ThAT AERiODYNAMTC COUPLING of Tr82 **MAIN WTNG ON THE ST.ABIL IZER' IcS' IMPORTANT FO9F L2XTBL-~ ** CDY MODES. '"HE FLLEXIBLE' BODY MODES USEB IN ITHE STU D Y ARE iMIE 4AT(URAL VIBRATION MODES. THE THEOREITICAL STUDY **WORKS HARD ON THE BCX METHOD FOR SUPERSONI1C FLOW. INGRAM, C.T. AND EICHENBAUM, F?.D., "A COMPA RISON O0F (> I FLIGET TEST MEASURED AND THEORETILCAL VERTICAL GJST RESPONSlv4 JOURNAL OF AIRCRAFT,. VOL. 6, NOV.-DEC. 1969, PP. 532-~53-o. IVERSEN, J.D. VN ~3ERNSTENS,"YAI 7I iULAT1AJ ~JF CRAFIL UNDER TLHE EFFECT CF VOLTEX WAKE TURVU'LENC;.~ A.VN ~S 0 LI CALCUL ANALOGIQUE, V 1th N. 3, JUL 1972s P 136- I'. dJffNSON, C. E. ANV9 SMill, L'jJ.R., "FlJTTER NA SAN'D 7j TESTING OF THEE F-/C/D/E A C.'.RAFT CARRYING MK '4 GR M-K 32 S- ' i 4~,C- ON Til MJF0 TB OA BD W I NG S TA ILT&S,w MC DO N ko7F L L A I aC RA FT c '), 1~ ~T'. C -U1,S3 14

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NELSCNt BC.., "CDY2IAMIC bEhAVIGOR CF AN A.iRCA-AFT ENCOtUNTEi ING AIRCEAFT WAKE TURBUILENCE," J AIRC. V. 13, NO. 9, SEPT' 1976-, P. NEULS, G.S., MAIER, H.G., LERWICK, T. R., ROBE, E.A., AND WEBSTER, I.J., "OPTIMUM FATIQUE SPECTRA," AERONAUTICAL SYSTEMS DIV., V., WRIGHT-PATTERSON AIR FORCE BASE, ASD-TR-61-235 (APRIL 1962). NEWBERRY, CLIFFORD F., "INTERACTION OF HANDLING QUALITIES, STABILITY, CONTROL AND LOAD ALLEVIATICN DEVICES ON STRUCTURAL LOADS," ADVISCRY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT, PARIS (FRANCE), REPT NO: AGARD-593, JUL 72. NORTH AMERICAN AVIATION INC, COLUMBIS, OHIO, "TURBULENCE STUDY OF A TRANSONIC WIND TUNNEL AND AN ANALYSIS AND TESTS OF AIRCRAFT RESPONSE TO TURBULENCE," REPT NO: NA-63H-636, 1 OCT 64. NORTON, PAUL SHERIDAN, "THE DETERMINATION OF THE DYNAMIC RESPONSE OF A SMALL SWEPT WING JET FIGHTER TO ATMOSPHERIC TURBULENCE USING THE POWER SPECTRUM METHOD OF ANALYSIS," MASTER'S THESIS, DEC 67. CEHMAN, W.I., "PRELIMINARY STUDY OF AIRPLANE- AUTOPILOT RESPONSE TO ATMOSPHERIC TURBULENCE," NASA SPEC PUBL 270 (PROC CONF ON AIRCRAFT SAFETY AND OPERATING PROBLEMS), HAMPTCN, VA, V. 1, MAY 4-6, 1971, PAPER 24, P. 323-34. 0' HARA, F. AND BURNHAM, J., "THE ATMOSPHERIC ENVIRONMENT, NOW AND FUTURE," THE AERONAUTICAL JOURNAL, VOL. 72, NO. 690, JUNE 1 S68. ONO, K., SCTOZAKI, T., TAKEUCHI, K. AND YAMANE, K., "AN OBSERVATIOP ON SPANWISE DISIRIBUTIOCN OF VEUTICAL ATMOSPHERIC TURBULENCE," ROYAL AIRCRAFT ESTABLISHMENT, FARNBORCUGH (ENGLAND)., REPT NO: RAE-LIB TRANS-1820, BR47555, JAN 75. CNO, K. AND YAMANE, K., "AN EXPERIMENTAL INVESTIGATION ON VERTICAL GUSTS AND THE AIRPLANE RESPONSE," NATIONAL AERASPACE LAB., TOKYO (JAPAN)., REPT NO: NAL-TR-89, 1965. OTTERSTEN, H., 1969: "ATMOSPHERIC STRUCTURE AND RADAR BACKSCATTERING IN CLEAR AIR." RADIO SCI., 4, 1179-1193. PAGE, C. H., "INSTANTANEOUS POWER SPECTRUM," JOURNAL OF APPLIED PHYSICS, VOL. 23, JAN. 1952, PP. 103-106. PANOFSKY, H.A., 1969: "INTERNAL ATMOSPHERIC TURBULENCF T BUILL. AMER. MET EOR. SOC., 50, 539-543. PARKINSON, R.C.H.: KELLY, D.W., "A DYNAMIC ANALYSIS OF %EROPLANES ENCOUNTERING VORTEX WAKE TURBULENCE," SYDNEY UNIV. (AUSTRALIA). DEPT OF AERONAUTICAL ENGINEERING., REPT NO: ATN-7301, JAN 73. PCHELKO, T.G. AND VASiL'YEVA, G.V., "TURBULENCE IN A CLEAR SKY," TR. GIDRCMETEROL. NAUCHNO-ISSLED, TSENT. SSSP, NO. 7, 1967., PP. 3015. PECKHAM, C.G., "A SUMMAtY OF ATMOSPHERIC TURBULENCE RECORDED BY NATO AIRCRAFT," ADVISORY GROUP FOR AEROSPACE RESEARCH AND 117

901 DEVELOPMENT, NEUILLY-SU R-SEINE, FRANCE, AGARD-,-586-71, SEVT, 1971. 902 0o3 PEELE, El AND STEINER, P., "SIMPLIFIED MET;OD OF ES. TATrNG THE 904 RESPONSE OF LIGHT AIRCRAFT TO CONTINUOUS ATMOSPHERIC TURBULENCE," 905 J AIRCRAFT, V. 7, NO. 5, SEPT-OCT 1970, P. 402-7. 906 907 PERROCHON, J., "STUDY OF ATMOSPHERIC TURBULENCE AT VEFY LOW 908 ALTITUDE, " ADVISCRY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT. 909 PARIS (FRANCE)., REPT NO: AGARD-440, APR 63. 910 911 PETERSEN, E. L., "A MODEL FOR THE SIMULATION OF 912 ATMOSHPERIC TURBULENCE," JOURNAL OF APPLIED METEOROLOGY, 913 VCL. 15, JUNE 1976, PP. 571-587 914. 915. PETRAKIS, JCHN AND MILLER, NELSON, "RESPONSES OF SMALL RIGI D X 916 CRAFT TO DISCRETE AND CCNTINUCUS GUST ANALYSIS," PHASE I, NATTONAL 917 AVIATION FACILITIES EXPERIMENTAL CENTER ATLANTIC CITY, N. J., 918 J* FEDERAL AVIATION ADMINISTRATION, WASHINGTON, C.D. SYSTEMS 919 RESEARCH AND DEVELOPMENT SERVICE., REPT NO: P AA-NI-74-44, DEC. 75. 920 921 922 PHILIPS, W. H., "GUST ALLEVIATION," NASA SPEC PUTBL 258 (PER923 FORMANCE AND DYNAMICS OF AERCSPACE VEHICLES), TROY, N.Y., 1971 924 PAPER 8, P. 505-53. 925 926 PHILLIPS, W. H., "STUDY OF A CONTROL SYSTEM TO ALLEVIATE AIP927 CRAFT RESPONSE TO HORIZONTAL AND VERTICAL GUSTS," NATIONAL AFRO928 NAUTICS AND SPACE ADMINISTRATION. LANGLEY RESEARCH CENTER, IANGLEY 929 STATION, VA., REPT NO: NASA-TN-D -7278, L-8844, DEC 73. 930 931 PI, W. S," AND, HWANG, C., "A NON-GAUSSIAN MCDEL FOR AIRCRAFT 932 RESPONSE ANALYSIS,"AlAA JOURNAL, VOL 16, NO. 7, JULY, 1978, 933 PP. 641-642. 934 935 PIERSOL, A.G., "INVESTIGATION OF THE STATISTICAL PROPERTIES 936 OF ATMOSPHERIC TURBULENCE DATA," TR MAC 28032-07, 1969, MEASURE937 MENT ANALYSIS CORP., MARINA DEL REY, CALIF. 938 939 PINSKER, W. J., "THEORETICAL ASSESSMENT OF THE GENERAL STABILI' 940 AND GUST RESPCNSE CHARACTERISTICS OF STOL AIRCRAFT," ROYAL 94" AIRCRAFT ESTABLISHMENT, bEDFORD (ENGLAND). AERODYNAMICS/FLTiiT 942 DEPT., REPT NC: ARC-R/M-3686, RAE-T R-71028, FEB. 71. 9435 944 PORT, W.G.A., "HIGH ALTITUDE GUST INVESTIGATION," ROYAL ArERONA c4J5 ESTABLISHMENT, FARNEOROUGH, ENGLAND, AERO 2341, NOV. 1949. o46 PRATT, K.G., "RESPONSE OF FLEXIBLE AIRPLANES TO ATMOSPiiERIC - T 3PR ATT, K.G., "RESPONSE OF FLEXIBLE AIRPLANES TO ATMOSP?5i R.C 4,9 TURBULENCE IN PERFORMANCE AND DYNAMICS OF AEROSPACE VEHICLES,".0 NASA SP-258, 1971, PP. 439-504. 952 PRATT, K.G., "A REVISED FORMULA FOR THE CALCULATION OF GUS' 953 LOADS," TN 2964, 1953, NACA. 9514 %55 PRESS, H., "AN APPROACH TO THE PREDICTION OF THE FPIQE NCY 956 DISTRIBUTION OF GUST LOADS ON AIRPLANES IN NORMAL OPERATIONS,'" 95 NACA, TN 2660, 1952. '945)8 959 PRESS, H., MEADOWS, M.T., AND HADLOCKI, I A RE-EVALATIAT(IN 960 OF DATA ON ATMOSPHERIC TURBULENCE AND AIRPLANE GUST LOADS FOR 118

1 APPLICATION IN SPECTRAL CALCULATIONS," NACA.EPT 1272 (1956). 2 3 PRESS, H., "ATMOSPHERIC TURBULENCE ENVIRONMENT WITH SPECIAL $4 EFBEENCE TO CONTINUOUS TURBULENCE," AGARD 115, APRIL-MAY 1957. 5 6 PRESS, H., AND MAZELSKY, B., " A STUDY OF THE APPLICATION OF 7 POWER-SPECTRAL METHODS CF GENERALIZED HARMONIC ANALYSIS TO GUST 8 LOADS ON AIRPLANES,' REPT 1172, 1954, NACA. 9 0 PRESS, H. AND TUKEY, J.W., "POWER SPECTRAL METHODS OF AJALYSIS 1 AND THE IR APPLICATION TO PROBLEMS IN AIRPLANE DYNAMICS," AGRBD 2 FLIGHT TEST MANUEL, VOL. IV, PT. IVC, (1956). 3 4 PRITCHARD, F.W., EASTERBROOK C, CC, MC VEHIL, G. E., "SPECTAL 5 AND EXCEEDANCE PROBABILITY MODELS OF ATMOSPHERIC TURBULENCE 6 FOR USE IN AIRCRAFT DESIGN AND OPERATION," AFFDL-TR-65-122, AIF7 FORCE FLIGHT DYNAMICS LABCRATORY, NOVEMBER, 1965. 8 9 PUCCINELLI, L., "CCMPARISONS BETWEEN ANALOGICAL AND NUMERICAL 0 METHODS FOR STUDYING THE RESPONSE OF AN AIRCRAFT TO GUSTS. 1 CONFRONTI FRA METODI ANAL OGICI E NUMERICI PER LO STUDIO DELLA PIS 2 POSTA DI UN VELIVOLO ALIA RAFFICA," PCLITECNICO DI MILANO (ITALY). 3 IST. DI INGEGNERIA AERCSPAZIALE., REPT NO: P UBL-97, 1970 4 5 RANKINE, ROBERT R. JR AND LEONDES, CORNELIUS T., "AIRPLANE YAW 6 PERTUREATIONS DUE TO VERTICAL AND SIDE GUSTS, J AIRON, V. 9, 7 N94, APR 1972, P. 316-3 17. 8 9 REEVES, P.M., JOPPA, R.G. AND GANZER, V.M., "A NON-GAUSSIAN MODEL O OF CCNTINUOUS ATMOSPHERIC TURBULENCE FOR USE IN AIRCRAFT DESTGN," 1 WASHINGTON UNIV., SEATTLE., SEPT NO: NASA-CR-2639, JAN 76. 2 3 REITER, E.R., 1969: "THE NATURE OF CLEAR AIR TURBULENCE: A FERVIEW. 4 "CLEAR AIR TURBULENCE AND ITS DETECTION," NEW YORK, PLENUM 5 PRESS, 7-33. REPORT OF THE NATIONAL COMMITTEE FOR CLEAR AIR TUR6 BULENCE TO THE FEDERAL COORDINATOR FOR METEOROLOGICAL SERVICES 7 AND SUPPORTING RESEARCH. U.S. DE PARIMENT OF COMMERCE, DEC. 1966. 8 AIMOSPHERIC TURBULENCE IN SEVERE STORMS AND CUMULUS CLOUDS," 9 O BEITER, E.R, "NATURE AND OBSERVATION OF HIGH-LEVEL TURBULENCE 1 ESPECIALLY IN CLEAR AIR," INSTITUTE OF THE AEROSPACE SCIENCES, IAS 2 PAPER NO. 63-81, PRESENTED AT THE IAS 31ST ANNUAL MEETING, NEW YORK, 3 NEW YORK, JAN. 21-23, 1963 4 5 RHYNE, R. H. AND STEINE", R., "PCWER SPECTRAL MEASUREMENT OF 6 ATMOSPHERIC TURBULENCE IN SEVERE STORMS AND CUMULUS CLOUDS," 7 TN D-2469, 1964, NASA. B 9 RICE, S.O., "MATHEMATICAL ANALYSIS OF RANDOM NOISE," BEZ L SYSTEf D TECHNICAL JOURNAL, VOL. 23, NC. 3, JULY 1944, PP. 282-332, 1 AND VCL. 24, NC. 1, J AN 1945, PP. 46-156. 2 3 RICH, M. J., JEPSON, W. D. AND BUFFALANO AC, C."STRUCTURAL DY4 NAMIC RESPONSE OF LARGE LOGISTIC V/STOL VEHICLES," TECHNICAL DCC5 UMENTARY REPT., JUN 62-F EB 64, APR 64. 6 7 RICHE, S.O., "MATHEMATICAL ANALYSIS OF RANDOM NOISE," BELL 8 SYSTEM TECHNICAL JOURNAL, VOL. 23, 1944, PP. 283-332; ALSO VOL. 9 24, 1945, PP. 46-156. 3 119

102 1 ROBERTS, J. Be., "STRUCTURAL FATIQUE UNDER NON-STATIONAiRY RhND0M 102 2 LOADING,"l JOU&,AL OF MECHANICAL ENGINEERING SCIENCE, VOL. Et '~023 NG. 4, 1966,r PP. 392-1405.o 1024 1025 RYAN, J.P.s, BEEENS, A.P.j, ROBERTSON, A.C., DCMINIC, R.J., AND 1026 ROLLE, K.C., "1MEDIUM ALTITUDE CRITICAL ATMOSPHERIC TURBULENCZE 1027 (MEDCAT) EATA PROCESSI'NG AND ANALYSIS," AFFDL-TR-71-82, JULY, -1028 1971, WRIGHT-PATTERSON AIR FORCE BASE, OHIO..1029 103 0 SAWDY, D. T., "ON THE TWO-DIMENSIONAL ATMOSPHERIC TURBULENCE, 1031' RESPONSE OF AN AIRPLANEa," KANSAS UNIV., LAWRENCE., REEPT NO: "TASA-1 032 CR-911161, 1966. -103 3.1034 SCHAENZERs G.r "T-HE INFLUENCE OF COUPLED NON-STATIONARkY GUSTS 1035 ON LOINGITUDINAL AIRCRAFT MOTION,"1 DEUTSCHE FORSCHUNGS, UND y;E? 1036 SUCHSANSTALT PIER LUFT - UIND RAUM4FAHRwt, BRUNSWICK (WEST GERMI-NY). 10637 INST. FUER FLIJGFUEHRUNG., REPT NO: DLR-FB-69-65, JUIN 69. *1038 1019 SEARS, W. R. AND SPARKS, 13.0., "ICN THE REACTION OF AN ELkSTIC lb~4O WING TO VERTI1CAL GUSTS,"l JOURNAL OF THE AERONAUTICAL SCIENCES, '1041 VOL. 9, 1941, PP. 64 -67. 10 42 1.04 3 SEARS,. W.R.,"4SOME ASPECTS OF NON-STA'T c;[ AROL 3 11.044 AND ITS PRACTICAL APPLICATIONS," JOUT. Of THE AERONAUTICAL 1045 SCIENCES, VOL. 8, NO. 3, 1941, PP. 104-108..1046 * 1047SHINOZUKA, N. AND YANG, J. N., "PEAK STRUCTURAL RESPONSE TO NO10 1-048 STATICNARY RANrOM EXCITATIONS." J SOUND VIBR* V. 16a, NO. ~4, JUNE 22,.1049 1971,w P. 505-17..1050 105-1 SHINOZUKA, M., "RANDOM PROCESSES WITH EVOLUTIONARY POWER,"1 105 2 TECH. REP! 4, SEPT., 1969, COLUMBIA UNIV. 10o53 1054 SIDWELL# K., "A METHOD FOR THE ANALYSIS OF NONLINEAFITIES TN 1 055 AIRCRAFT DYNAMIC RESPONSE TO ATMOSPHERIC TURBULENCE," NATIONAL 1 056 AERONAUTICS AND SPACE ADMINISTRATION. LANGLEY RESEARCH CENTER, 105 7 LANGLEY STATION, VA., REPT NO: NASA -TN-D-8265s L-10L487, NOV 76. "0)58 '1O SKELTON, GRANT 2.,i "INVESTIGATION OF THE EFFECTS OF GiUSTS ON 1O'U V/STCL CRAFT IN TRANSITION AND HOVER," HONEYWELL INC ST PAUL MN RESEARCH DEPTs REPT NO: 12060-FR1, OCT 68. C)SMETANA, F. 0. AND CARDEN, R. K., "AN ANALYTICAL STUDY OF H it) 4 PONSE OF A CONSTANT-ATTITUDE AIRCRAFT TO ATMOSPHERIC TURBUL1ENCE, 1 06 5. NORTH CAROLINA STATE UNIV., RALEIGHo REPT NO: NASA-CR-220~4,t M A F,7U I b, 6 DURING LANDING APPROACH," NATIONAL AERONAUTICS AND) SPACE ADMNTSTSR.A SNYDER, C. T., "ANALCG STUDY OF THE LONGITUDINAL RESPO3 OI F 06 9 A SWEPT-WING TRANSPORT AIRPLANE TO WIND SHEAR AND SUSTAINED GUSTS 1070 DURING LANDING APPROACH,"l NATIONAL AERONAUTICS AND SPAC%.E ADMITNISTRA~ 07 I TION. AMES RESEARCH CENTER, MOFFETT FIELD, CALIF., REPT NO: 1.012 NASA-'N —4477, APR 68. 1 07 3 ~4014SPEAKMAN, JERRY D.,. BONFILI, HUBERT P.,v HILLE, HAROLD K. kND I 0 7. JOHN N N, "CREW EXPOSURE TO VIBRATION IN THE F-4C AIRCRAFT D'IRING 1076 LOW-ALTITUDE, HIGH-SPEED FLIGHT,"f AEROSPACE MEDICAL RBS-EURCH iltB,zl o0 7 7 WRIGHT-PATTERSON AFB, OHIO, REPT NO: AMRL-TR-70-99, JAN 7-1. 1078 10 79 1i08 0 SPILLANE, K.T., "THE WINTER JETSTREAM OF AUJSTR~ALIA AND 17 —'-Q I 20

1.U.. S L A L,GAZ iNE VOL. i, F S 96 6, 3 4 SPIE, JAiES K. "VALIDATION OF N ~ GUST DESIGN PROCEDURES FOP: IL~[TARY TRANSPORTS," LCCKHEED-GEORGIA CO MARIETTA, fEPT NO: i LG73ER0153, NOV 73. STEINER, R., "A REVIEW OF NASA HIGH ALTITUDE 47 C'LEAB AIR TUREULENCE SAMPLING PROGRAMS," JOURNAL OF AIRCRAFT, VOL. 3 3 JAN. 1966, PP. 48-52. J STEINER, RCY, "tA REVIEW OF NASA HIGH-ALTITUDE CLEAR AIR I TURBULENCE SAMPLING PROGRAMS," J. AIRCRAFT, VOL. 3, NO. 1, FEB. 1966, PP. 48-52 * A GOOC REVIEW OF CLEAR AIR TURBULENCE UP TO 1966. SEEMS ** TO OVERSIMPLIFY A LITTLE, BUT HAS SOME GOOD CURVES FOR ** PROBABILITY OF EXCEEDING GIVEN GUST VELOCITIES PER MILE ~* TRAVELLED. GIVES ESTIMATES FOR TURBULENT PATCH SIZE. STENTON, 1. E., "ANALYTICAL STUDY OF THE RESPONSE OF A CCONSTANTATTITUDE AIRCRAFT TC ATMOSPHERIC TURBULENCE." NASA CONTRACT REPCR-1621 AUG 1970, 121 P. STENTON, T. E., "THEORETICAL FREQUENCY RESPONSE FUNCTIONS AND POWER SPECTRA OF THE XB-70 RESPONSE TO ATMOSPHERIC TURBULENCE, NORTH AMERICAN ROCKWELL CORP., LOS ANGELES, CALIF., REPT NO: NASA-CR-1621, AUG 70. SWAIMN, ROCERT L. AND CONNORS, ALONZO J., "EFFECTS IF GUT VELOCITY SPATIAL DISTRIEUTIONS ON LATERAL-DIRECTIONAL RESPCNSE OF A VTOL AIRCRAFT," AIR FORCE FLIGHT DYNAMICS LAB WRIGHT-PATTERSON AFB, OHIO, REPT NO: AFFDL-TR-67-93, JUN 67. SWANSON, R., "PRACTICAL FATIQUE LOCADINGS FOR AERONAUTICAL STRUCTURES," AIAA PAPER N. 64-568. TAYLOR, J., "BUFFETING TURBULENCE," AGARD MANUAL ON AIRCRAFT LOADS, PERGAMON, NEW YORK, 1965, PP. 245-260. TAYLOR, 3., "RELATIVE FEEQUENCY CF OCCURENCE OF DIFFERENT NORMAL ACCELERATIONS AT THE CENTRE OF GRAVITY OF AIRCRAFT IN TURBULENCE," ROYAL AIRCRAFT ESTABLISHMENT, FARNBOROUGH, (ENGLAND), REPT. NO: RAE-TR-71169, AUG. 1971 THEISEN, J.G. AND HAAS, J., "TURBULENCE UPSET AND OTHER STUDIES ON JET TRANSPORTS," JOURNAL OF AIRCRAFT, VOL. 5, NO. 4, JULY-AUG 'i968, PP. 344-353. THEODORSEN, T., "GENERAL THEORY OF AERODYNAMIC INSTABILITY AND THE MECHANISM OF FLUTTER," REPT 496, 1935, NACA. VAN ATTA, C. W. ANE CHEN, W.Y., "STRUCTURE FUNCTIONS OF TURBULENCE IN THE ATMOSPHERIC BOUNDARY LAYER OVER THE OCEAN," JOURNAL OF FLUID MECHANICS, VOL. 44, 1970, PP. 145-159. VANDERVAART, J. C., "THE IMPULSE RESPONSE METHOD FOR THE CALCULATION OF STATISTICAL PROPERTIES OF AIRCRAFT FLYING IN RANDOM ATMOSPHERIC TURBULENCE", TECHNISCHE HOGESCHOOL, DELFT (NETHERLANDS). DEPT CF AEROSPACE ENGINEERING., REPT NC: VTH-197, NOV 75. VERDON, JOSEPH M., STEINER, ROY, "RESPONSE OF A RIGID AfRCRAFT TO NONSTATIONARY ATMOSPHERIC TURBULENCE." AIAA J, V. 11, NO. 8, 121

1141 AUG. 1973, PP. 1086-1092. 114. ** THIS PAPER EXTENDS EABLIER WORK ON RESPONSE TO NONSTATiO'ARYE 1143 ** TURBULENCE BY ALLOWING A MORE GENERAL MODULATING ENVELOPE? OF 4 044 ** THE RANDOM VELOCITY FIELD. THIS WAS MOTIVATED BY EXPERI'ENTAT. 1145 ** RESULTS WHICH DID NOT AGREE WITH PREVIOUS THEORY. IT DOES 1146 ** IMPROVE THE RESULTS, BUT IS SOMEWHAT OF A CURVE-FITTING 1147 ** APPROACH, SINCE THE MODULATING SIGNAL IS ABSTRACTLY CHOSEN 1148 ** AS A SINE WAVE MULTIPLIED BY A STEP FUNCTION. THE PAPER 1149 ** ONLY CONSIDERS PLUNGING OF A RIGID AIRCRAFT. 1150 1151 VINNICHENKO, N. K., PINUS, N. Z., AND SHUR, G. N., "STUDY OF 1152 CLEAR SKY TURBULENCE IN THE STRATOSPHERE," TRUDY TSENTRAL-NOY 1153 AEROLOGICHESKOY OBSERVATORII, FIZIKA SVOBODNOY ATMOSFERY, NO. 100, 1154 1970, PP. 86-98. 1155 1156 VON KARMAN, T., "PROGRESS IN THE STATISTICAL THEORY OF TURBH1157 LENCE," TURBULENCE CLASSIC PAPERS ON STATISTICAL THEORY, INTER1158 STATE PUBLISHERS, NEW YCBK, 1961, PP. 162-173. 1159 1160 VON KARMAN, T. AND HOWARTH, L., "ON THE STATISTICAL THEORY 1161 OF ISCTROPIC TURBULENCE," PROC. ROY. SOC., VOL. CIXIV-A, (LON3DOt) 1162 PP. 193-194 (1938). 1163 1164 WACO, DAVID E. "VARIATICN OF WT:LJENCE WITH ALTITUDE 1165 TO 70,000 FT," J. AIRCRAFT, VOL. 13, NO. 12, DEC. 1976, PP. 981-986 1166 ** A CONCISE REVIEW OF EXPERIMENTAL MEASUREMENTS OF TURBULENCE. 1167 ** SUMMARIZES ALL RESULTS FOR PERCENTAGE OF TIME IN FLIGHT t168 ** AT TURBULENCE LEVELS ABOVE O.08G (2FPS) REPEATED EXCURSIONS. 1169 ** ALSO GIVES RULES FOR RATIO OF MODERATE TO LIGHT TURBULENCE 1170 ** WHEN OVER VARIOUS TERRAIN. SHOWS HOW DEFINITION OF 1171 ** TURBULENCE IN G'S AFFECTS PERCENTAGE OF FLIGHI DISTANCE 1172 ** DENOTED AS TURBULENT. 1173 1174 WAIKINS, C. E., WOCLSTON, D. S., AND CUNNINGHAM, H. J., "A 1175 SYSTEMATIC KERNEL FUNCTION PROCEDURE FOR DETERMINING AERODYNAITC 1176 FORCES ON OSCIILATING OR STEADY FINITE WINGS AT SUBSONIC SPEEDS," 1177 TR R-48,1959, NASA. 1178 179 WEBER R. N. F., "THE SYNOPTIC-AEROLOGICAL CCNDITIONS FOR THE 114 8OCCURRENCE OF CLEAR AIR TURBULENCE, 12TH ORGANIZATION SCIENTITIFQJE 1 i ET TECHNIQUE IN TERNATICNALE DU VOL A VOILE, CONGRESS, ALPINE, (82 TEX., 1970, PP. 366, 423-425 4 WILLIAMS, D.A., "MEASUREMENT OF THE SYMMETRIC RESPONSE OF THE Mta. S. 760 PARIS AIRCRAFT TO ATMOSPHERIC TURBULENCE, COLLEGE OF l E: AERONAUTICS, CRANFIELD (ENGLAND). REPT NO: COA-AERO-211, 1969. 'Ja WILSON, R. J., LOVE, B. J., AND LARSCN, R. R, "EVALSUATL DIO 1i39 OP EFFECTS OF HIGH ALTITUDE TURBULENCE ENCOUNTERS ON THE X3-70 10 AIRPLANEw NASA TN-D-6457, JULY 1971. i92 WITHERS, DOUGLAS R. JR., "THE INFLUENCE OF FOLL, PITCH, AND e93 YAW RATE PERTURBATIONS ON THE ALPHA-BETA STABILITY ENVELOPE OF 1 194 THE E-4D AIRCRAFT," AIR FORCE INST OF TECH, WRIGHT-PATTESSON AFB, 1195 OHIO, SCHOOL OF ENGINEERING, REPT NO: GAE/MC/75D-10, JAN 76. S19 7 WOODS, J. D., 1969: "ON BICHARDSCN'S NUMBER AS A CRITEPIN F P ^ 1<.8 LAMINAR- TURBULENT TRANSITION IN THE OCEAN AND ATMOSPHERE. PA.O 1199 SCI., VOL. 4, PP. 1289-1298. 1200 122

1 YASUE, ~M~, A SL' U D 1 0`~ cU ST S PC N SE i~ A c?2L>T 2 C 3U 31SNG FL IGHiT, O MA 3, AC iIU~S1ETTS IN33T. 0F TECH1., CAMBRIDGE. Ai2RC3 E LtSTIC AND STgUCTUR ES PES~ ARCH L A3L REPT NO: N ASA -C R- 137517, 4 ASL.L-TR-174-10 AUG 714. o YFF#, J., "RATIONAL CALCULATION OF DESIGq GUST LOADS IN RELATION 7 TO PBESENT AND PROPOSED AIRWORTHINESS REQUIREMENTS,." ROYAL 8 NETHERLANDS AIRCRAFT FACTORIES FOKKER., AMSTERDAM.,, REPT NO: F'CK9 K66, 1973. 0 1 YOST, JAMES D., JACKSON, WAYNIE B., AND SALTER, L.,"TMPROVED 2 METHCICS OF ATMOSPHERIC TURBULENCE PREDICTION FOR AIRCRAFT DESIGN 3 AND OPERATION." JOURNAL AIRCR 9, NO. 14, APR 1972, PP. 266-272. S ZBROZEK, J. K., "THEORETICAL STUDY OF THE ROLLINkG EESPONSE SOF AIRCRAFT TO TURBULENT AlR, ADVISORY GROUP FOR AERONAUTICAL PEISEARCH AND DEVELOPMENT, PARIS (FRANCE)., REPT NO: AGARD-373, 3 APR 61. ZBORZEK, J. Ke, "THEORETICAL STUDY OF THE ROLLING3 RESPONSE OF AIRCRAFT TO TURBULENT AIR, AERONAUTICAL RESEARCH CC)UNCIL (GIT. 3RIT.), REPT NO: ARC-R +M-TN-AERO-2753, APR 61 ZBOIRZEK, J. K., "ATMOSPHERIC GUSTS, PRESENT STATE OFTE AIT AND FURTHER RESEARCH," JOURNAL OF THE ROYAL AERONAUTICAL S OC IET Y, VOL. 69, NO. 649, JAN. 1965. ZBORZEKO J. K-a, "THE RELATIONSHIP BETWEEN DISCRETE GUST AND PO)WER SPECTRA PRESENTATIONS OF ATMOSPHERIC TURBULENCE, WITH A SU,\3IGSTED) MODEL OF LOW-ALTITUDE TURBULENCE,"l AERONAUTICAL RESEARCH COUNCTL R & M. 3216 (MARCH 1960). FILE 123 b1 4o It 4.1 4. I& * 1* I& * * 'A * * 4. 4, 4. 4. * *.&')&A * -..4 4.& A 4..4.4.4.4.0 4. w& 4..4. 4..L & 4.4. 'k& *:.44..4.4..44. 4. 4.4.4.4. &4 &.&.& -1 L. -,,J..&. & 4.4.4.4.4.4 4. 4.